Elementary functions: algorithms and implementation
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2006
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014616315&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXII, 265 S. graph. Darst. |
| ISBN: | 9780817643720 0817643729 |
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| 245 | 1 | 0 | |a Elementary functions |b algorithms and implementation |c Jean-Michel Muller |
| 250 | |a 2. ed. | ||
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Datensatz im Suchindex
| _version_ | 1819321386430103552 |
|---|---|
| adam_text | CONTENTS LIST OF FIGURES XI LIST OF TABLES XV PREFACE TO THE SECOND
EDITION XIX PREFACE TO THE FIRST EDITION XXI 1 INTRODUCTION 1 SOME BASIC
THINGS ABOUT COMPUTER ARITHMETIC 9 ....................... 2.1
FLOATING-POINT ARITHMETIC 9 ..................... 2.1.1 FLOATING-POINT
FORMATS 9 ........................ 2.1.2 ROUNDING MODES 11 .............
2.1.3 SUBNORMAL NUMBERS AND EXCEPTIONS 13
............................... 2.1.4 ULPS 14 ................ 2.1.5
FUSED MULTIPLY-ADD OPERATIONS 15 .......... 2.1 -6 TESTING YOUR
COMPUTATIONAL ENVIRONMENT 16 ............. 2.1.7 FLOATING-POINT
ARITHMETIC AND PROOFS 17 2.1.8 MAPLE PROGRAMS THAT COMPUTE
DOUBLE-PRECISION ......................... APPROXIMATIONS 17
..................... 2.2 REDUNDANT NUMBER SYSTEMS 19 .................
2.2.1 SIGNED-DIGIT NUMBER SYSTEMS 19 ............. 2.2.2 RADIX-2
REDUNDANT NUMBER SYSTEMS 21 I ALGORITHMS BASED ON POLYNOMIAL
APPROXIMATION ANDLOR TABLE LOOKUP. MULTIPLE-PRECISION EVALUATION OF
FUNCTIONS 25 3 POLYNOMIAL OR RATIONAL APPROXIMATIONS 27 .............
3.1 LEAST SQUARES POLYNOMIAL APPROXIMATIONS 28 .....................
3.1.1 LEGENDRE POLYNOMIALS 29 .................... 3.1.2 CHEBYSHEV
POLYNOMIALS 29 ....................... 3.1.3 JACOBI POLYNOMIALS 31
CONTENTS ..................... 3.1.4 LAGUERRE POLYNOMIALS 31 3.1.5 USING
THESE ORTHOGONAL POLYNOMIALS IN ANY INTERVAL .... 31 ............ 3.2
LEAST MAXIMUM POLYNORNIAL APPROXIMATIONS 32
............................. 3.3 SOME EXAMPLES 33
......................... 3.4 SPEED OF CONVERGENCE 39
........................... 3.5 REMEZ S ALGORITHM 41
....................... 3.6 RATIONAL APPROXIMATIONS 46 ...............
3.7 ACTUAL COMPUTATION OF APPROXIMATIONS 50 .............. 3.7.1 GETTING
GENERAL APPROXIMATIONS 50 3.7.2 GETTING APPROXIMATIONS WITH SPECIAL
CONSTRAINTS ...... 51 3.8 ALGORITHMS AND ARCHITECTURES FOR THE
EVALUATION OF POLYNOMIALS . 54 .......................... 3.8.1 THE
E-METHOD 57 ......................... 3.8.2 ESTRIN S METHOD 58 3.9
EVALUATION ERROR ASSUMING HORNER S SCHEME IS USED ....... 59 3.9.1
EVALUATION USING FLOATING-POINT ADDITIONS AND .........................
MULTIPLICATIONS 60 3.9.2 EVALUATION USING FUSED MULTIPLY-ACCUMULATE
........................... INSTRUCTIONS 64
.............................. 3.10 MISCELLANEOUS 66 4 TABLE-BASED
METHODS 67 ............................... 4.1 INTRODUCTION 67
........................ 4.2 TABLE-DRIVEN ALGORITHMS 70 4.2.1 TANG S
ALGORITHM FOR EXP(X) IN IEEE FLOATING-POINT ARITHMETIC 71
.......................... 4.2.2 LN(X) ON [L, 21 72
........................ 4.2.3 SIN(X) ON [O, ~/4] 73
..................... 4.3 GAL S ACCURATE TABLES METHOD 73 4.4 TABLE
METHODS REQUIRING SPECIALIZED HARDWARE .......... 77 4.4.1 WONG AND
GOTO S ALGORITHM FOR COMPUTING ............................ LOGARITHMS
78 4.4.2 WONG AND GOTO S ALGORITHM FOR COMPUTING
........................... EXPONENTIALS 81 .................. 4.4.3
ERCEGOVAC ET AL. S ALGORITHM 82 ............. 4.4.4 BIPARTITE AND
MULTIPARTITE METHODS 83 .......................... 4.4.5 MISCELLANEOUS
87 5 MULTIPLE-PRECISION EVALUATION OF FUNCTIONS 89
............................... 5.1 INTRODUCTION 89 5.2 JUST A FEW WORDS
ON MULTIPLE-PRECISION MULTIPLICATION ...... 90 ......................
5.2.1 KARATSUBA S METHOD 91 ...................... 5.2.2 FET-BASED
METHODS 92 ............ 5.3 MULTIPLE-PRECISION DIVISION AND SQUARE-ROOT
92 .................. 5.3.1 NEWTON-RAPHSON ITERATION 92 CONTENTS VII 5.4
ALGORITHMS BASED ON THE EVALUATION OF POWER SERIES
............................... 94 5.5 THE ARITHMETIC-GEOMETRIC (AGM)
MEAN ............... 95 5.5.1 PRESENTATION OF THE AGM
.................... 95 5.5.2 COMPUTING LOGARITHMS WITH THE AGM
............ 95 5.5.3 COMPUTING EXPONENTIALS WITH THE AGM ........... 98
5.5.4 VERY FAST COMPUTATION OF TRIGONOMETRIC FUNCTIONS ..... 98 I1 SHIF
T-AND-ADD ALGORITHMS 101 6 INTRODUCTION TO SHIFT-AND-ADD ALGORITHMS 103
6.1 THE RESTORING AND NONRESTORING ALGORITHMS ............ 105 6.2
SIMPLE ALGORITHMS FOR EXPONENTIALS AND LOGARITHMS ....... 109 6.2.1 THE
RESTORING ALGORITHM FOR EXPONENTIALS .......... 109 6.2.2 THE RESTORING
ALGORITHM FOR LOGARITHMS ........... 111 6.3 FASTER SHIFT-AND-ADD
ALGORITHMS ................... 113 6.3.1 FASTER COMPUTATION OF
EXPONENTIALS ............. 113 6.3.2 FASTER COMPUTATION OF LOGARITHMS
.............. 119 6.4 BAKER S PREDICTIVE ALGORITHM
..................... 122 6.5 BIBLIOGRAPHIC NOTES
.......................... 131 7 THE CORDIC ALGORITHM 133 7.1
INTRODUCTION ............................... 133 7.2 THE CONVENTIONAL
CORDIC ITERATION ................. 134 7.3 SCALE FACTOR COMPENSATION
...................... 139 7.4 CORDIC WITH REDUNDANT NUMBER SYSTEMS AND
A VARIABLE FACTOR 141 7.4.1 SIGNED-DIGIT IMPLEMENTATION
................. 142 7.4.2 CARRY-SAVE IRNPLEMENTATION
.................. 143 7.4.3 THE VARIABLE SCALE FACTOR PROBLEM
............... 143 7.5 THE DOUBLE ROTATION METHOD .....................
144 7.6 THE BRANCHING CORDIC ALGORITHM .................. 146 7.7 THE
DIFFERENTIAL CORDIC ALGORITHM ................. 150 7.8 COMPUTATION OF
COS-I AND SINPL USING CORDIC .......... 153 7.9 VARIATIONS ON CORDIC
......................... 156 8 SOME OTHER SHIFT-AND-ADD ALGONTHMS 157
8.1 HIGH-RADIX ALGORITHMS ........................ 157 8.1.1 ERCEGOVAC S
RADIX-16 ALGORITHMS ............... 157 8.2 THE BKM ALGORITHM
.......................... 162 8.2.1 THE BKM ITERATION
....................... 162 8.2.2 COMPUTATION OF THE EXPONENTIAL
FUNCTION (E-MODE) .... 162 8.2.3 COMPUTATION OF THE LOGARITHM FUNCTION
(L-MODE) ..... 166 CONTENTS 8.2.4 APPLICATION TO THE COMPUTATION OF
ELEMENTARY ............................. FUNCTIONS 167 I11 RANGE
REDUCTION. FINAL ROUNDING AND EXCEPTIONS 171 9 RANGE REDUCTION 173
............................... 9.1 INTRODUCTION 173 9.2 CODY AND
WAITE S METHOD FOR RANGE REDUCTION .......... 177 ............. 9.3
FINDING WORST CASES FOR RANGE REDUCTION? 179 ......... 9.3.1 A FEW BASIC
NOTIONS ON CONTINUED FRACTIONS 179 ....... 9.3.2 FINDING WORST CASES
USING CONTINUED FRACTIONS 180 ............. 9.4 THE PAYNE AND HANEK
REDUCTION ALGORITHM 184 .............. 9.5 THE MODULAR RANGE REDUCTION
ALGORITHM 187 ..................... 9.5.1 FIXED-POINT REDUCTION 188
.................... 9.5.2 FLOATING-POINT REDUCTION 190 .............
9.5.3 ARCHITECTURES FOR MODULAR REDUCTION 190
........................... 9.6 ALTERNATE METHODS 191 10 FINAL ROUNDING
193 ............................... 10.1 INTRODUCTION 193
.............................. 10.2 MONOTONICITY 194 ........... 10.3
CORRECT ROUNDING: PRESENTATION OF THE PROBLEM 195
........................... 10.4 SOME EXPERIMENTS 198 ............. 10.5
A PROBABILISTIC APPROACH TO THE PROBLEM 198 ..........................
10.6 UPPER BOUNDS ON M 202 ............. 10.7 OBTAINED WORST CASES FOR
DOUBLE-PRECISION 203 ...................... 10.7.1 SPECIAL INPUT VALUES
203 ...................... 10.7.2 LEFEVRE S EXPERIMENT 203 11
MISCELLANEOUS 11.1 EXCEPTIONS ............................... 11.1.1
NANS .............................. 11.1.2 EXACT RESULTS
.......................... 11.2 NOTES ON XY
.............................. 11.3 SPECIAL FUNCTIONS, FUNCTIONS OF
COMPLEX NUMBERS ....... 12 EXAMPLES OF IMPLEMENTATION 225 12.1 EXAMPLE
1: THE CYRIX FASTMATH PROCESSOR ..... : ........ 225 12.2 THE INTEL
FUNCTIONS DESIGNED FOR THE ITANIUM PROCESSOR ..... 226
......................... 12.2.1 SINE AND COSINE 227
............................ 12.2.2 ARCTANGENT 228
......................... 12.3 THE LIBULTIM LIBRARY 229
.......................... 12.4 THE CRLIBM LIBRARY 229 ....... 12.4.1
COMPUTATIONOF SIN(X) OR COS(X) (QUICKPHASE) 230 CONTENTS IX
..................... 12.4.2 COMPUTATION OF LN(X) 230
........................ 12.5 SUN S LIBMCR LIBRARY 231 .......... 12.6
THE HP-UX COMPILER FOR THE ITANIUM PROCESSOR 231 BIBLIOGRAPHY 233 INDEX
261
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| discipline | Informatik Mathematik |
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| id | DE-604.BV021295549 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:32:43Z |
| institution | BVB |
| isbn | 9780817643720 0817643729 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014616315 |
| oclc_num | 60500353 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-706 DE-83 DE-11 DE-384 DE-898 DE-BY-UBR DE-355 DE-BY-UBR |
| owner_facet | DE-824 DE-703 DE-706 DE-83 DE-11 DE-384 DE-898 DE-BY-UBR DE-355 DE-BY-UBR |
| physical | XXII, 265 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Birkhäuser |
| record_format | marc |
| spellingShingle | Muller, Jean-Michel 1961- Elementary functions algorithms and implementation Algorithmes Algoritmos larpcal Fonctions (Mathématiques) - Informatique Matemática (processamento de dados) larpcal Datenverarbeitung Algorithms Functions Data processing Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Elementare Funktion (DE-588)4302697-7 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4042805-9 (DE-588)4302697-7 |
| title | Elementary functions algorithms and implementation |
| title_auth | Elementary functions algorithms and implementation |
| title_exact_search | Elementary functions algorithms and implementation |
| title_full | Elementary functions algorithms and implementation Jean-Michel Muller |
| title_fullStr | Elementary functions algorithms and implementation Jean-Michel Muller |
| title_full_unstemmed | Elementary functions algorithms and implementation Jean-Michel Muller |
| title_short | Elementary functions |
| title_sort | elementary functions algorithms and implementation |
| title_sub | algorithms and implementation |
| topic | Algorithmes Algoritmos larpcal Fonctions (Mathématiques) - Informatique Matemática (processamento de dados) larpcal Datenverarbeitung Algorithms Functions Data processing Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Elementare Funktion (DE-588)4302697-7 gnd |
| topic_facet | Algorithmes Algoritmos Fonctions (Mathématiques) - Informatique Matemática (processamento de dados) Datenverarbeitung Algorithms Functions Data processing Numerisches Verfahren Numerische Mathematik Elementare Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014616315&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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