Computer arithmetic algorithms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Natick, Mass.
Peters
2002
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 281 S. graph. Darst. |
| ISBN: | 1568811608 |
Internformat
MARC
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| 245 | 1 | 0 | |a Computer arithmetic algorithms |c Israel Koren |
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Datensatz im Suchindex
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| adam_text | Titel: Computer arithmetic algorithms
Autor: Koren, Israel
Jahr: 2002
CONTENTS
FORWORD TO THE SECOND EDITION xi
PREFACE xiii
1 CONVENTIONAL NUMBER SYSTEMS 1
1.1 The Binary Number System 1
1.2 Machine Representations of Numbers 2
1.3 Radix Conversions 4
1.4 Representations of Negative Numbers 6
1.5 Addition and Subtraction 13
1.6 Arithmetic Shift Operations 15
1.7 Exercises 16
1.8 References 17
2 UNCONVENTIONAL FIXED-RADIX NUMBER SYSTEMS 19
2.1 Negative-Radix Number Systems 19
2.2 A General Class of Fixed-Radix Number Systems 21
viii Contents
2.3 Signed-Digit Number Systems 23
2.4 Binary SD Numbers 27
2.5 Exercises 32
2.6 References 33
3 SEQUENTIAL ALGORITHMS FOR MULTIPLICATION
AND DIVISION 35
3.1 Sequential Multiplication 35
3.2 Sequential Division 39
3.3 Nonrestoring Division 42
3.4 Square Root Extraction 48
3.5 Exercises 50
3.6 References 52
4 BINARY FLOATING-POINT NUMBERS 53
4.1 Preliminaries 53
4.2 Floating-Point Operations 59
4.3 Choice of Floating-Point Representation 65
4.4 The IEEE Floating-Point Standard 67
4.5 Round-off Schemes 71
4.6 Guard Digits 76
4.7 Floating-Point Adders 81
4.8 Exceptions 84
4.9 Round-off Errors and Their Accumulation 87
4.10 Exercises 89
4.11 References 91
5 FAST ADDITION 93
5.1 Ripple-Carry Adders 93
5.2 Carry-Look-Ahead Adders 95
5.3 Conditional Sum Adders 99
5.4 Optimality of Algorithms and Their Implementations 102
5.5 Carry-Look-Ahead Addition Revisited 106
5.6 Prefix Adders 109
Contents
5.7 Ling Adders 110
5.8 Carry-Select Adders 113
5.9 Carry-Skip Adders 116
5.10 Hybrid Adders 119
5.11 Carry-Save Adders 124
5.12 Pipelining of Arithmetic Operations
5.13 Exercises 135
5.14 References 138
IX
132
6 HIGH-SPEED MULTIPLICATION 141
6.1 Reducing the Number of Partial Products 141
6.2 Implementing Large Multipliers Using Smaller Ones 149
6.3 Accumulating the Partial Products 145
6.4 Alternative Techniques for Partial Product Accumulation 157
6.5 Fused Multiply-Add Unit 165
6.6 Array Multipliers 167
6.7 Optimality of Multiplier Implementations 174
6.8 Exercises 176
6.9 References 179
7 FAST DIVISION 181
7.1 SRT Division 181
7.2 High-Radix Division 187
7.3 Speeding Up the Division Process 198
7.4 Array Dividers 203
7.5 Fast Square Root Extraction 206
7.6 Exercises 209
7.7 References 210
8 DIVISION THROUGH MULTIPLICATION 213
8.1 Division by Convergence 213
8.2 Division by Reciprocation 218
8.3 Exercises 222
8.4 References 223
Contents
9 EVALUATION OF ELEMENTARY FUNCTIONS 225
9.1 The Exponential Function 226
9.2 The Logarithm Function 229
9.3 The Trigonometric Functions 232
9.4 The Inverse Trigonometric Functions 235
9.5 The Hyperbolic Functions 238
9.6 Bounds on the Approximation Error 239
9.7 Speed-up Techniques 241
9.8 Other Techniques for Evaluating Elementary Functions 243
9.9 Exercises 244
9.10 References 245
10 LOGARITHMIC NUMBER SYSTEMS 247
10.1 Sign-Logarithm Number Systems 247
10.2 Arithmetic Operations 249
10.3 Comparison to Binary Floating-Point Numbers 252
10.4 Conversions to/from Conventional Representations 253
10.5 Exercises 255
10.6 References 256
11 THE RESIDUE NUMBER SYSTEM 259
11.1 Preliminaries 259
11.2 Arithmetic Operations 261
11.3 The Associated Mixed-Radix System 264
11.4 Conversion of Numbers from/to the Residue System 266
11.5 Selecting the Moduli 267
11.6 Error Detection and Correction 269
11.7 Exercises 274
11.8 References 275
INDEX 277
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:00Z |
| institution | BVB |
| isbn | 1568811608 |
| language | English |
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| physical | XV, 281 S. graph. Darst. |
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| publisher | Peters |
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| spelling | Koren, Israel Verfasser aut Computer arithmetic algorithms Israel Koren 2. ed. Natick, Mass. Peters 2002 XV, 281 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithmus (DE-588)4001183-5 gnd rswk-swf Computerarithmetik (DE-588)4135485-0 gnd rswk-swf Computerarithmetik (DE-588)4135485-0 s Algorithmus (DE-588)4001183-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017438637&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koren, Israel Computer arithmetic algorithms Algorithmus (DE-588)4001183-5 gnd Computerarithmetik (DE-588)4135485-0 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4135485-0 |
| title | Computer arithmetic algorithms |
| title_auth | Computer arithmetic algorithms |
| title_exact_search | Computer arithmetic algorithms |
| title_full | Computer arithmetic algorithms Israel Koren |
| title_fullStr | Computer arithmetic algorithms Israel Koren |
| title_full_unstemmed | Computer arithmetic algorithms Israel Koren |
| title_short | Computer arithmetic algorithms |
| title_sort | computer arithmetic algorithms |
| topic | Algorithmus (DE-588)4001183-5 gnd Computerarithmetik (DE-588)4135485-0 gnd |
| topic_facet | Algorithmus Computerarithmetik |
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