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Muller J.-M. — Elementary functions: algorithms and implementation
Muller J.-M. — Elementary functions: algorithms and implementation

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Название: Elementary functions: algorithms and implementation

Автор: Muller J.-M.

Аннотация:

This book gives the concepts and background necessary to understand and build algorithms for computing elementary functions, presenting and structuring the algorithms (hardware- oriented as well as software-oriented), and discusses issues related to the accurate floating-point implementation. The purpose is not to give "cookbook recipes" that allow one to implement some given function, but to provide the reader with the knowledge that is necessary to build, or adapt, algorithms to their specific computing environment. Topics and Features: * background material reviewed in Chapter 2, Computer Arithmetic * polynomial and rational approximations * table based methods * shift-and-add algorithms thoroughly covered in Part Two * CORDIC algorithm * range reduction and accuracy covered in Part Three * Web site for the book containing additional resources and selected code The book provides an up-to-date presentation of the information needed to understand and accurately use mathematical functions and algorithms in computational work and design. Graduates, professionals and researchers in scientific computing, software engineering, and computer engineering will find the book a useful reference and resource.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 204

Добавлена в каталог: 15.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accurate tables method      58
Adaptation of coefficients      43
Addition      13
Agarwal      2 163
AMD K5      48
Antelo      124
Arithmetic-geometric mean      173 181
Avizienis' algorithm      14 15
Bailey      181
Baker's predictive algorithm      90
Base      9
BKM, algorithm      131
BKM, E-mode      133
BKM, iteration      133
BKM, L-mode      133 137
Bogacki      124
Borrow-save, addition      16
Borrow-save, number system      16
Branching cordic algorithm      115
Braune      47
Brent      173 181
Briggs      4 71 72
Carry propagation      13
Carry-save, addition      16
Carry-save, computation of exponentials      86
Carry-save, number system      15 82 111
Cavallaro      125
CELEFUNT      48
chebyshev      30
Chebyshev approximation to $e^x$      26
Chebyshev approximation to functions      23
Chebyshev polynomials      23 26
Chebyshev theorem      25 26
Chebyshev theorem for rational approximations      34
Cody      1 48 147
Complex arguments      48
Continued fractions      149
CoRDIC      5 76 101
CORDIC on line      125
CORDIC, arcos      122
CORDIC, arcsin      122
CORDIC, branching      115
CORDIC, decimal      124
CORDIC, differential      118—120
CORDIC, double rotation      112
CORDIC, hyperbolic mode      105
CORDIC, iteration      105
CORDIC, rotation mode      102 106
CORDIC, scale factor compensation      107
CORDIC, vectoring mode      105 106
Correct rounding      2 163
Cyrix, 83D87      62
Cyrix, FastMath      41
Daggett      124
Dawid and Meyr      118
Delosme      112 124
DeLugish      98
Deprettere      109 125
Despain      107
Dewilde      109
Differential CORDIC      118—120
Discrete base      76 102
Distillation      12
Double rotation method      112
Dunham      39
E-method      45
Ercegovac      3 119 125 174
Ercegovac, E-method      45
Ercegovac, radix-16 algorithms      127
Exact rounding      2 12 165
Exceptions      12 175—177
Exponential, Baker's method      97
Exponential, BKM      133
Exponential, fast shift and add algorithm      81
Exponential, multiple precision      181 182
Exponential, radix-16      127
Exponential, restoring algorithm      73 77
Exponential, table-driven      55
Exponential, Tang      55
Exponential, Wong and Goto      65
Feldstein      169
Final rounding      163
Floating-point arithmetic      9—13
Floating-point arithmetic, test of      13
floating-point division      35
Flynn      35
Fourier transform      101
Fused MAC      43
Gal, accurate tables method      58
Goldberg      9
Goodman      169
Gradual underflow      12
Hamada      36
Hanek      147
Hartley transform      101
Haviland      107
Hekstra      125
Hemkumar      125
Hewlett Packard's HP      35 101
High-radix algorithms      127
Horner's scheme      43
Hsiao      124
hu      124 125
IBM/370      58
IEEE-754 standard      1 10—12 62 175
infinity      12
Intel, 8087      1 9 101 124
Intel, Pentium      15
Interval arguments      48
Interval arithmetic      12
Jacobi approximation to functions      23
Jacobi polynomials      23
Kahan      1 9 147 149 176
Koren      3 35
Kota      125
Kramer      47
Krishnamurthy      76
Kropa      124
Kuki      1
Lang      3 125 174
Least maximum approximation to $e^x$      26
Least maximum approximation to functions      24
Least squares approximations      22
Legendre approximation to $e^x$      25
Legendre approximation to functions      23
Legendre polynomials      23 25
Lin      125
Lindemann theorem      167
Linhardt      98
Litvinov      34
Logarithm, BKM      137
Logarithm, fast shift and add algorithm      88
Logarithm, multiple precision      181 182
Logarithm, restoring algorithm      79 80
Logarithm, table-driven      57
Logarithm, Tang      57
Logarithm, Wong and Goto      62
Luk      125
Lynch      175
MACHAR      13
Malcolm      13
Maple      2 38
Meggitt      76 98
Miller      98
Minimax approximation to $e^x$      26
Minimax approximations      24
Modular range reduction      158
Monotonicity      2 163 164
Motorola, 68881      124
Motorola, Power PC      43
Multiple precision      147 180
Multiple precision, exponentials      181 182
Multiple precision, logarithms      181
Naganathan      124
Nan (not a number)      12 176
Nesterenko      172
Nonrestoring algorithm      76 102
Normalized numbers      10
Oberman      35
Okabe      1
Omondi      3
Orthogonal polynomials      22
Pade approximants      35
Paranoia      13
Payne      147
Pocket calculators      10 101 124
Polynomial approximations      21—25 29 31 35
Polynomial approximations, least maximum      24
Polynomial approximations, least squares      22
Polynomial approximations, particular form      39
Polynomial approximations, speed of convergence      31
Polynomial evaluation      43
Polynomial evaluation, adaptation of coefficients      43
Polynomial evaluation, E-method      45
Polynomial evaluation, Estrin's method      47
Polynomial evaluation, Horner's scheme      43
Polynomier      47
Power function      178
Predictive algorithm      90
Pseudodivision      76 98
Pseudomultiplication      76 98
RADIX      9
Radix-16 algorithms      127
Range limits      2 163
Range reduction      5 56 143—149 152—154 156 158 176
Range reduction, additive      143
Range reduction, Cody and Waite      148
Range reduction, modular      158
Range reduction, multiplicative      143
Range reduction, Payne and Hanek      154
Range reduction, positive      158
Range reduction, redundant      158
Range reduction, symmetrical      158
Range reduction, Tang      56
Range reduction, worst cases      149
Rational approximations      34—36
Rational approximations, equivalent expressions      36
Rational approximations, particular form      39
Reduced argument      143
Redundant number systems      13 15 81 82 88 95 109 111 112 114 115 131 161
remez      34
Restoring algorithm      74
Robertson diagrams      82 83 88 109 128 134 135
Rounding modes      10—12 165 166
Salamin      181
Sarkar      76
Scale factor compensation      107
Schmid      124
Schulte and Swartzlander      168
Shift-and-add, algorithms      71 73 76 81 88 98 101 127
Shift-and-add, exponentials in a redundant number system      81
Shift-and-add, logarithms in a redundant number system      88
Signed zeroes      12
Signed-digit, computation of exponentials      83
Signed-digit, number system      14 15 82 111
Sine and cosine, accurate tables      60
Sine and cosine, CORDIC      101
Sine, special polynomial approximation      39
Sine, table-driven      58
Sine, Tang      58
sips      125
Specker      98
SRT division      86
Subnormal numbers      12 176
SVD      101
Swartzlander      3 175
Symmetry      2 163
Table maker's dilemma      163 166
Table maker's dilemma, deterministic approach      171
Table maker's dilemma, probabilistic approach      168
Table-based methods      51
Table-driven algorithms      53 55 57 58
Takagi      81 112 114
Tang table-driven algorithms      53
Taylor expansions      29 181
Timmermann      125
Trivedi      119
Tuszinsky      107
Udo      109
ULP (unit in the last place)      13 37 65
Voider      98 101
Voider, CORDIC iteration      101
Waite      1 147
Waldschmidt      172
Walther      101
Walther, CORDIC iteration      105
Weierstrass theorem      24
Weight function      21—23 39—41
Wong and Goto's algorithm      62
Zinaty      35
Ziv      167
Zuras      173
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