Mercurial > cpython-lru_cache-weakref

annotate Python/pymath.c @ 55725:ec8d25e0500a legacy-trunk

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#6677: mention "deleting" as an alias for removing files.
author Georg Brandl <georg@python.org>
date Mon, 24 Aug 2009 17:24:27 +0000
parents 96d82facd890
children 2ab08c919648
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 #include "Python.h"
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2
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3 #ifdef X87_DOUBLE_ROUNDING
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4 /* On x86 platforms using an x87 FPU, this function is called from the
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5 Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point
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6 number out of an 80-bit x87 FPU register and into a 64-bit memory location,
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7 thus rounding from extended precision to double precision. */
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8 double _Py_force_double(double x)
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9 {
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10 volatile double y;
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11 y = x;
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12 return y;
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13 }
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14 #endif
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15
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16 #ifndef HAVE_HYPOT
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17 double hypot(double x, double y)
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18 {
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19 double yx;
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20
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21 x = fabs(x);
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22 y = fabs(y);
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23 if (x < y) {
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24 double temp = x;
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25 x = y;
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26 y = temp;
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27 }
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28 if (x == 0.)
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29 return 0.;
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30 else {
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31 yx = y/x;
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32 return x*sqrt(1.+yx*yx);
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33 }
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34 }
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35 #endif /* HAVE_HYPOT */
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36
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37 #ifndef HAVE_COPYSIGN
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38 double
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39 copysign(double x, double y)
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40 {
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41 /* use atan2 to distinguish -0. from 0. */
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42 if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) {
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43 return fabs(x);
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44 } else {
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45 return -fabs(x);
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46 }
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47 }
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48 #endif /* HAVE_COPYSIGN */
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49
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50 #ifndef HAVE_ROUND
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51 double
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52 round(double x)
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53 {
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54 double absx, y;
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55 absx = fabs(x);
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56 y = floor(absx);
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57 if (absx - y >= 0.5)
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58 y += 1.0;
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59 return copysign(y, x);
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60 }
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61 #endif /* HAVE_ROUND */
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62
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63 #ifndef HAVE_LOG1P
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64 #include <float.h>
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65
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66 double
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67 log1p(double x)
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68 {
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69 /* For x small, we use the following approach. Let y be the nearest
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70 float to 1+x, then
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71
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72 1+x = y * (1 - (y-1-x)/y)
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73
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74 so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,
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75 the second term is well approximated by (y-1-x)/y. If abs(x) >=
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76 DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
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77 then y-1-x will be exactly representable, and is computed exactly
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78 by (y-1)-x.
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79
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80 If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
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81 round-to-nearest then this method is slightly dangerous: 1+x could
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82 be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
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83 case y-1-x will not be exactly representable any more and the
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84 result can be off by many ulps. But this is easily fixed: for a
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85 floating-point number |x| < DBL_EPSILON/2., the closest
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86 floating-point number to log(1+x) is exactly x.
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87 */
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88
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89 double y;
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90 if (fabs(x) < DBL_EPSILON/2.) {
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91 return x;
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92 } else if (-0.5 <= x && x <= 1.) {
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93 /* WARNING: it's possible than an overeager compiler
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94 will incorrectly optimize the following two lines
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95 to the equivalent of "return log(1.+x)". If this
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96 happens, then results from log1p will be inaccurate
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97 for small x. */
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98 y = 1.+x;
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99 return log(y)-((y-1.)-x)/y;
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100 } else {
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101 /* NaNs and infinities should end up here */
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102 return log(1.+x);
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103 }
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104 }
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105 #endif /* HAVE_LOG1P */
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106
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107 /*
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108 * ====================================================
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109 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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110 *
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111 * Developed at SunPro, a Sun Microsystems, Inc. business.
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112 * Permission to use, copy, modify, and distribute this
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113 * software is freely granted, provided that this notice
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114 * is preserved.
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115 * ====================================================
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116 */
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117
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118 static const double ln2 = 6.93147180559945286227E-01;
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119 static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
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120 static const double two_pow_p28 = 268435456.0; /* 2**28 */
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121 static const double zero = 0.0;
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122
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123 /* asinh(x)
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124 * Method :
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125 * Based on
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126 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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127 * we have
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128 * asinh(x) := x if 1+x*x=1,
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129 * := sign(x)*(log(x)+ln2)) for large |x|, else
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130 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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131 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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132 */
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133
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134 #ifndef HAVE_ASINH
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135 double
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136 asinh(double x)
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137 {
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138 double w;
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139 double absx = fabs(x);
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140
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141 if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
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142 return x+x;
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143 }
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144 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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145 return x; /* return x inexact except 0 */
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146 }
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147 if (absx > two_pow_p28) { /* |x| > 2**28 */
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148 w = log(absx)+ln2;
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149 }
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150 else if (absx > 2.0) { /* 2 < |x| < 2**28 */
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151 w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
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152 }
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153 else { /* 2**-28 <= |x| < 2= */
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154 double t = x*x;
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155 w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
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156 }
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157 return copysign(w, x);
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158
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159 }
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160 #endif /* HAVE_ASINH */
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161
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162 /* acosh(x)
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163 * Method :
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164 * Based on
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165 * acosh(x) = log [ x + sqrt(x*x-1) ]
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166 * we have
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167 * acosh(x) := log(x)+ln2, if x is large; else
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168 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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169 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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170 *
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171 * Special cases:
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172 * acosh(x) is NaN with signal if x<1.
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173 * acosh(NaN) is NaN without signal.
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174 */
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175
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176 #ifndef HAVE_ACOSH
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177 double
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178 acosh(double x)
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179 {
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180 if (Py_IS_NAN(x)) {
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181 return x+x;
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182 }
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183 if (x < 1.) { /* x < 1; return a signaling NaN */
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184 errno = EDOM;
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185 #ifdef Py_NAN
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186 return Py_NAN;
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187 #else
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188 return (x-x)/(x-x);
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189 #endif
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190 }
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191 else if (x >= two_pow_p28) { /* x > 2**28 */
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192 if (Py_IS_INFINITY(x)) {
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193 return x+x;
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194 } else {
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195 return log(x)+ln2; /* acosh(huge)=log(2x) */
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196 }
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197 }
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198 else if (x == 1.) {
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199 return 0.0; /* acosh(1) = 0 */
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200 }
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201 else if (x > 2.) { /* 2 < x < 2**28 */
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202 double t = x*x;
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203 return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
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204 }
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205 else { /* 1 < x <= 2 */
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206 double t = x - 1.0;
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207 return log1p(t + sqrt(2.0*t + t*t));
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208 }
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209 }
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210 #endif /* HAVE_ACOSH */
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211
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212 /* atanh(x)
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213 * Method :
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214 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
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215 * 2.For x>=0.5
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216 * 1 2x x
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217 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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218 * 2 1 - x 1 - x
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219 *
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220 * For x<0.5
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221 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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222 *
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223 * Special cases:
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224 * atanh(x) is NaN if |x| >= 1 with signal;
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225 * atanh(NaN) is that NaN with no signal;
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226 *
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227 */
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228
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229 #ifndef HAVE_ATANH
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230 double
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231 atanh(double x)
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232 {
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233 double absx;
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234 double t;
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235
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236 if (Py_IS_NAN(x)) {
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237 return x+x;
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238 }
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239 absx = fabs(x);
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240 if (absx >= 1.) { /* |x| >= 1 */
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241 errno = EDOM;
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242 #ifdef Py_NAN
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243 return Py_NAN;
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244 #else
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245 return x/zero;
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246 #endif
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247 }
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248 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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249 return x;
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250 }
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251 if (absx < 0.5) { /* |x| < 0.5 */
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252 t = absx+absx;
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253 t = 0.5 * log1p(t + t*absx / (1.0 - absx));
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254 }
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255 else { /* 0.5 <= |x| <= 1.0 */
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256 t = 0.5 * log1p((absx + absx) / (1.0 - absx));
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257 }
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258 return copysign(t, x);
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259 }
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Christian Heimes <christian@cheimes.de>
parents:
diff changeset
260 #endif /* HAVE_ATANH */