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annotate lib/expl.c @ 7292:17785d5bede0

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Fix docstrings
author Sergey Poznyakoff <gray@gnu.org.ua>
date Sun, 10 Sep 2006 11:52:44 +0000
parents a48fb0e98c8c
children c115624bf99a
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1 /* Emulation for expl.
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2 Contributed by Paolo Bonzini
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3
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4 Copyright 2002, 2003 Free Software Foundation, Inc.
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5
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6 This file is part of gnulib.
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7
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8 This program is free software; you can redistribute it and/or modify
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9 it under the terms of the GNU General Public License as published by
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10 the Free Software Foundation; either version 2, or (at your option)
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11 any later version.
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12
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13 This program is distributed in the hope that it will be useful,
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14 but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 GNU General Public License for more details.
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17
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18 You should have received a copy of the GNU General Public License along
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19 with this program; if not, write to the Free Software Foundation,
5848
a48fb0e98c8c *** empty log message ***
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20 Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
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21
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22 #include <float.h>
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23 #include <math.h>
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24
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25 #include "mathl.h"
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26
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27 static const long double C[] = {
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28 /* Chebyshev polynom coeficients for (exp(x)-1)/x */
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29 #define P1 C[0]
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30 #define P2 C[1]
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31 #define P3 C[2]
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32 #define P4 C[3]
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33 #define P5 C[4]
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34 #define P6 C[5]
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35 0.5L,
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36 1.66666666666666666666666666666666683E-01L,
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37 4.16666666666666666666654902320001674E-02L,
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38 8.33333333333333333333314659767198461E-03L,
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39 1.38888888889899438565058018857254025E-03L,
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40 1.98412698413981650382436541785404286E-04L,
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41
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42 /* Smallest integer x for which e^x overflows. */
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43 #define himark C[6]
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44 11356.523406294143949491931077970765L,
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45
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46 /* Largest integer x for which e^x underflows. */
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47 #define lomark C[7]
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48 -11433.4627433362978788372438434526231L,
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49
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50 /* very small number */
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51 #define TINY C[8]
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52 1.0e-4900L,
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53
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54 /* 2^16383 */
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55 #define TWO16383 C[9]
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56 5.94865747678615882542879663314003565E+4931L};
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57
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58 long double
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59 expl (long double x)
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60 {
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61 /* Check for usual case. */
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62 if (x < himark && x > lomark)
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63 {
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64 int exponent;
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65 long double t, x22;
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66 int k = 1;
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67 long double result = 1.0;
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68
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69 /* Compute an integer power of e with a granularity of 0.125. */
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70 exponent = (int) floorl (x * 8.0L);
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71 x -= exponent / 8.0L;
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72
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73 if (x > 0.0625)
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74 {
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75 exponent++;
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76 x -= 0.125L;
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77 }
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78
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79 if (exponent < 0)
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80 {
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81 t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
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82 exponent = -exponent;
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83 }
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84 else
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85 t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */
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86
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87 while (exponent)
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88 {
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89 if (exponent & k)
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90 {
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91 result *= t;
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92 exponent ^= k;
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93 }
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94 t *= t;
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95 k <<= 1;
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96 }
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97
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98 /* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
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99 with maximum error in [-2^-16-2^-53,2^-16+2^-53]
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100 less than 4.8e-39. */
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101 x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
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102
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103 return result + result * x22;
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104 }
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105 /* Exceptional cases: */
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106 else if (x < himark)
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107 {
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108 if (x + x == x)
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109 /* e^-inf == 0, with no error. */
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110 return 0;
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111 else
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112 /* Underflow */
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113 return TINY * TINY;
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114 }
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115 else
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116 /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
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117 return TWO16383*x;
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118 }
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119
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120 #if 0
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121 int
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122 main (void)
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123 {
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124 printf ("%.16Lg\n", expl(1.0L));
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125 printf ("%.16Lg\n", expl(-1.0L));
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126 printf ("%.16Lg\n", expl(2.0L));
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127 printf ("%.16Lg\n", expl(4.0L));
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128 printf ("%.16Lg\n", expl(-2.0L));
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129 printf ("%.16Lg\n", expl(-4.0L));
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130 printf ("%.16Lg\n", expl(0.0625L));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
131 printf ("%.16Lg\n", expl(0.3L));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
132 printf ("%.16Lg\n", expl(0.6L));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
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133 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
134 #endif