Mathematik für Wirtschaftswissenschaftler: das ECOMath-Handbuch
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer Gabler
2012
|
| Edition: | 2. Aufl. |
| Series: | Lehrbuch
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 1. Aufl. als zweibändiges Werk u.d.T.: ECOMath1 und ECOMath2 |
| Physical Description: | XII, 1120 S. graph. Darst. |
| ISBN: | 9783642299841 3642299849 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804149385841344512 |
|---|---|
| adam_text | IMAGE 1
TABLE OF CONTENTS
1 INTRODUCTION AND OVERVIEW 1
1.1 BACKGROUND 1
1.2 MOTIVATIONS 3
1.3 RESEARCH OBJECTIVES AND SCOPE 4
1.4 THESIS OUTLINE 5
2 IMPROVEMENT OF STANDARD AND NON-STANDARD FLOATING-POINT OPERATIONS 7
2.1 STATE-OF-THE-ART 8
2.1.1 CHIP DESIGN AND FUNCTIONALITY 8
2.1.2 IMPROVEMENT OF PERFORMANCE AND EFFICIENCY AT RUNTIME 9
2.1.3 ENHANCEMENT OF DESIGNS AND ALGORITHMS OF BASIC ARITHMETIC UNITS .
9 2.2 FLOATING-POINT OPERATION ALGORITHM AND ANALYSIS 10
2.2.1 COMMON FUNCTIONS 11
2.2.1.1 UNPACKING FUNCTION 11
2.2.1.2 COMPARISON FUNCTION 11
2.2.1.3 NORM FUNCTION 12
2.2.1.4 UNPACKING3 FUNCTION 14
2.2.2 STANDARD OPERATION 14
2.2.2.1 FLOATING-POINT ADDITION/SUBTRACTION 14
2.2.2.2 FLOATING-POINT MULTIPLICATION 16
2.2.3 NON-STANDARD OPERATION 17
2.2.3.1 FLOATING-POINT PRODUCT-OF-SUM OPERATION 17
2.2.3.2 FLOATING-POINT SUM-OF-PRODUCT OPERATION 19
2.3 DESIGN AND ENHANCEMENT OF THE FUNCTION AND OPERATION 21
2.3.1 LEADING-ONE-DETECTION BASED O N BINARY-TREE ALGORITHM 21
2.3.2 RIGHT/LEFT SHIFTING FUNCTION 23
2.3.3 PARTIAL LINEAR INTEGER MULTIPLIER BASED ON PIPELINING ARCHITECTURE
. . 24
2.4 IMPLEMENTATION A N D INVESTIGATION OF FLOATING-POINT OPERATOR 25
2.4.1 SYNTHESIS RESULT CORRESPONDING TO STAGE NUMBERS 25
XV
HTTP://D-NB.INFO/1029442746
IMAGE 2
XVI
TABLE OF C O N T E N T S
2.4.1.1 FLOATING-POINT ADDER 25
2.4.1.2 FLOATING-POINT MULTIPLIER 26
2.4.1.3 FLOATING-POINT POS 26
2.4.1.4 FLOATING-POINT SOP 26
2.4.2 COMPARISON AND STATISTICAL ANALYSIS IN ACCURACY 26
2.5 DESIGN AND ARCHITECTURE OF FLOATING-POINT ARITHMETIC ACCELERATOR 31
2.5.1 DESIGN AND ARCHITECTURE 31
2.5.2 MICRO-INSTRUCTION AND TIMING DIAGRAM 32
2.5.3 PERFORMANCE ANALYSIS 34
2.6 SUMMARY 38
3 CORDIC ALGORITHM AND ELEMENTARY FUNCTIONS BASED ON NON-REDUNDANT
METHOD 39 3.1 INTRODUCTION 40
3.2 STATE-OF-ART 41
3.2.1 HIGH RADIX CORDIC METHOD 42
3.2.2 PARALLEL CORDIC ROTATION METHOD 42
3.2.3 REDUNDANT NUMBER REPRESENTATION METHOD 43
3.2.4 ROTATION EXTENSION METHOD 43
3.3 ROTATION-EXTENSION CORDIC ALGORITHM 44
3.3.1 CONVENTIONAL CORDIC 45
3.3.2 DOUBLE-ROTATION CORDIC 46
3.3.3 TRIPLE-ROTATION CORDIC 47
3.3.4 ACCURACY EVALUATION 47
3.3.5 CONVERGENCE & ACCURACY TRADE-OFF 50
3.4 THE CIRCULAR COORDINATE SYSTEM 55
3.4.1 CONVERGENCE 56
3.4.2 ACCURACY 58
3.5 THE HYPERBOLIC COORDINATE SYSTEM 61
3.5.1 CONVERGENCE 62
3.5.2 ACCURACY 64
3.6 THE LINEAR COORDINATE SYSTEM 70
3.6.1 CONVERGENCE 70
3.6.2 ACCURACY 71
3.7 UNIFIED CORDIC 77
3.8 EXTENSION FUNCTIONS 77
3.8.1 NATURAL LOGARITHM 77
3.8.2 SQUARE ROOT 79
3.9 PROBLEM OF CONVERGENCE RANGE ON ELEMENTARY FUNCTIONS 82
IMAGE 3
TABLE O F C O N T E N T S XVII
3.9.1 PRE/POSTPROCESSING WITH MATHEMATICAL IDENTITIES METHOD 82
3.9.2 SEQUENTIAL INDEX EXTENSION METHOD 84
3.10 SUMMARY 85
4 DESIGN AND ARCHITECTURE FOR VLSI IMPLEMENTATION O F AN ARITHMETIC UNIT
87
4.1 STATE-OF-ART 88
4.1.1 DESIGN AND IMPLEMENTATION OF FLOATING-POINT ACCELERATOR A N D PRO
CESSOR 89
4.1.2 ACCELERATOR AND PROCESSOR BASED ON CORDIC 89
4.2 UNIFIED MICRO-ROTATION ARCHITECTURE OF CORDIC 90
4.2.1 DESIGN AND ARCHITECTURE 91
4.2.2 RESOURCE CONSUMPTION AND PERFORMANCE ANALYSIS 94
4.3 A HIGH PRECISION CORDIC CORE 95
4.3.1 ALGORITHM 95
4.3.2 COMPUTATIONAL TIME INVESTIGATION 95
4.3.3 PERFORMANCE COMPARISON 100
4.4 DATA CONVERSION 103
4.4.1 FIXED-POINT REPRESENTATION 103
4.4.2 FLOATING-TO-FIXED ALGORITHM 104
4.4.3 FIXED-TO-FLOATING ALGORITHM 107
4.5 DESIGN AND ARCHITECTURE OF A ARITHMETIC ACCELERATOR 112
4.5.1 DESIGN AND ARCHITECTURE 112
4.5.1.1 MICRO-INSTRUCTION SET 112
4.5.1.2 A FETCH-AND-DECODE UNIT 113
4.5.1.3 A CORDIC UNIT 115
4.5.1.4 A WRITEBACK UNIT 116
4.5.2 IMPLEMENTATION AND PERFORMANCE ANALYSIS 118
4.6 DESIGN AND ARCHITECTURE OF A RECONFIGURABLE STREAMING PROCESSOR 120
4.6.1 DESIGN AND ARCHITECTURE 120
4.6.2 CORE CONFIGURATION, MICRO-INSTRUCTION, AND TIMING DIAGRAM . . . .
121
4.6.3 IMPLEMENTATION AND PERFORMANCE ANALYSIS 124
4.7 ARITHMETIC CO-PROCESSOR/PROCESSOR COMPARISON 126
4.8 SUMMARY 128
5 VERIFICATION ON THE CLOSED-LOOP CONTROL SYSTEM FOR HEAVY ION
SYNCHROTRON AP PLICATION 131
5.1 SYSTEM BACKGROUND 132
5.2 BEAM PHASE CONTROL 133
IMAGE 4
XVIII TABLE OF C O N T E N T S
5.3 PHASE-MAGNITUDE COMPUTATION 134
5.3.1 STATE-OF-THE-ART 134
5.3.2 ARCHITECTURE FOR PHASE-MAGNITUDE COMPUTING 134
5.3.3 VERIFICATION AND SIMULATION 137
5.3.3.1 TEST PATTERN 1 138
5.3.3.2 TEST PATTERN 2 142
5.4 SUMMARY 146
6 CONCLUDING REMARKS 147
6.1 CONTRIBUTION OF THE WORK 147
6.2 DIRECTION FOR FUTURE WORK . 1 4 8
A HARDWARE FOR SCIENTIFIC AND ENGINEERING APPLICATIONS 149
6 ELEMENTARY ROTATION ANGLE O F THE DOUBLE-ROTATION AND TRIPLE-ROTATION
CORDIC METHODS 151
REFERENCES 169
LIST O F O W N PUBLICATIONS 171
INDEX 173
CURRICULUM VITAE 177
|
| any_adam_object | 1 |
| author | Dietz, Hans M. 1951- |
| author_GND | (DE-588)123671248 |
| author_facet | Dietz, Hans M. 1951- |
| author_role | aut |
| author_sort | Dietz, Hans M. 1951- |
| author_variant | h m d hm hmd |
| building | Verbundindex |
| bvnumber | BV040349091 |
| classification_rvk | QH 110 SK 980 |
| ctrlnum | (OCoLC)823229510 (DE-599)DNB1023059525 |
| dewey-full | 330.0151 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330.0151 |
| dewey-search | 330.0151 |
| dewey-sort | 3330.0151 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. Aufl. |
| format | Book |
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| spelling | Dietz, Hans M. 1951- Verfasser (DE-588)123671248 aut Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch Hans M. Dietz 2. Aufl. Berlin [u.a.] Springer Gabler 2012 XII, 1120 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lehrbuch 1. Aufl. als zweibändiges Werk u.d.T.: ECOMath1 und ECOMath2 Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s 1\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025203173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dietz, Hans M. 1951- Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4123623-3 |
| title | Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch |
| title_auth | Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch |
| title_exact_search | Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch |
| title_full | Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch Hans M. Dietz |
| title_fullStr | Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch Hans M. Dietz |
| title_full_unstemmed | Mathematik für Wirtschaftswissenschaftler das ECOMath-Handbuch Hans M. Dietz |
| title_short | Mathematik für Wirtschaftswissenschaftler |
| title_sort | mathematik fur wirtschaftswissenschaftler das ecomath handbuch |
| title_sub | das ECOMath-Handbuch |
| topic | Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Wirtschaftsmathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025203173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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