Computer arithmetic and validity: theory, implementation, and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
©2013
|
| Edition: | 2nd ed |
| Series: | De Gruyter studies in mathematics
33 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | 8.6 Scalar product computation units (SPUs) Print version record |
| Physical Description: | 1 online resource (456 pages) |
| ISBN: | 3110301792 9783110301731 9783110301793 |
Staff View
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| 505 | 8 | |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 | |
| 505 | 8 | |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 | |
| 505 | 8 | |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 | |
| 505 | 8 | |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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| author | Kulisch, Ulrich |
| author_facet | Kulisch, Ulrich |
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| 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 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 |
| ctrlnum | (OCoLC)857276812 (DE-599)BVBBV043034040 |
| dewey-full | 004.0151 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004.0151 |
| dewey-search | 004.0151 |
| dewey-sort | 14.0151 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| edition | 2nd ed |
| format | Electronic eBook |
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| id | DE-604.BV043034040 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:34Z |
| institution | BVB |
| isbn | 3110301792 9783110301731 9783110301793 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028458688 |
| oclc_num | 857276812 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (456 pages) |
| psigel | ZDB-4-EBA 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 theory, implementation, and applications Ulrich Kulisch 2nd ed Berlin ; Boston De Gruyter ©2013 1 online resource (456 pages) txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics 33 8.6 Scalar product computation units (SPUs) Print version record 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 Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd rswk-swf Gleitkommarechnung (DE-588)4157582-9 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 Erscheint auch als Druck-Ausgabe Kulisch, Ulrich Computer Arithmetic and Validity : Theory, Implementation, and Applications http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=604262 Aggregator Volltext 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 theory, implementation, and applications 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 Intervallalgebra (DE-588)4139152-4 gnd Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd Gleitkommarechnung (DE-588)4157582-9 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4135485-0 (DE-588)4139152-4 (DE-588)4127444-1 (DE-588)4157582-9 (DE-588)4042805-9 |
| title | Computer arithmetic and validity theory, implementation, and applications |
| title_auth | Computer arithmetic and validity theory, implementation, and applications |
| title_exact_search | Computer arithmetic and validity theory, implementation, and applications |
| title_full | Computer arithmetic and validity theory, implementation, and applications Ulrich Kulisch |
| title_fullStr | Computer arithmetic and validity theory, implementation, and applications Ulrich Kulisch |
| title_full_unstemmed | Computer arithmetic and validity theory, implementation, and applications Ulrich Kulisch |
| title_short | Computer arithmetic and validity |
| title_sort | computer arithmetic and validity theory implementation and applications |
| title_sub | theory, implementation, and applications |
| 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 Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd Gleitkommarechnung (DE-588)4157582-9 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 Richtigkeit von Ergebnissen Gleitkommarechnung Numerische Mathematik |
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| work_keys_str_mv | AT kulischulrich computerarithmeticandvaliditytheoryimplementationandapplications |