Mercurial > cpython-lru_cache-weakref

annotate Python/pymath.c @ 49955:878d40468c4e legacy-trunk

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Issue #4384: Added logging integration with warnings module using captureWarnings(). This change includes a NullHandler which does nothing; it will be of use to library developers who want to avoid the "No handlers could be found for logger XXX" message which can appear if the library user doesn't configure logging.
author Vinay Sajip <vinay_sajip@yahoo.co.uk>
date Wed, 03 Dec 2008 23:22:58 +0000
parents 922b9e03b260
children 79a6c63ac5b0 f9f2ed79b00f
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 #ifndef HAVE_HYPOT
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4 double hypot(double x, double y)
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5 {
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6 double yx;
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7
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8 x = fabs(x);
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9 y = fabs(y);
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10 if (x < y) {
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11 double temp = x;
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12 x = y;
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13 y = temp;
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14 }
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15 if (x == 0.)
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16 return 0.;
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17 else {
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18 yx = y/x;
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19 return x*sqrt(1.+yx*yx);
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20 }
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21 }
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22 #endif /* HAVE_HYPOT */
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23
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24 #ifndef HAVE_COPYSIGN
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25 static double
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26 copysign(double x, double y)
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27 {
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28 /* use atan2 to distinguish -0. from 0. */
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29 if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) {
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30 return fabs(x);
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31 } else {
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32 return -fabs(x);
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33 }
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34 }
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35 #endif /* HAVE_COPYSIGN */
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36
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37 #ifndef HAVE_LOG1P
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38 #include <float.h>
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39
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40 double
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41 log1p(double x)
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42 {
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43 /* For x small, we use the following approach. Let y be the nearest
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44 float to 1+x, then
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45
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46 1+x = y * (1 - (y-1-x)/y)
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47
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48 so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,
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49 the second term is well approximated by (y-1-x)/y. If abs(x) >=
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50 DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
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51 then y-1-x will be exactly representable, and is computed exactly
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52 by (y-1)-x.
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53
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54 If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
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55 round-to-nearest then this method is slightly dangerous: 1+x could
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56 be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
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57 case y-1-x will not be exactly representable any more and the
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58 result can be off by many ulps. But this is easily fixed: for a
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59 floating-point number |x| < DBL_EPSILON/2., the closest
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60 floating-point number to log(1+x) is exactly x.
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61 */
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62
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63 double y;
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64 if (fabs(x) < DBL_EPSILON/2.) {
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65 return x;
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66 } else if (-0.5 <= x && x <= 1.) {
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67 /* WARNING: it's possible than an overeager compiler
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68 will incorrectly optimize the following two lines
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69 to the equivalent of "return log(1.+x)". If this
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70 happens, then results from log1p will be inaccurate
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71 for small x. */
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72 y = 1.+x;
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73 return log(y)-((y-1.)-x)/y;
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74 } else {
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75 /* NaNs and infinities should end up here */
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76 return log(1.+x);
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77 }
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78 }
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79 #endif /* HAVE_LOG1P */
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80
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81 /*
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82 * ====================================================
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83 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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84 *
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85 * Developed at SunPro, a Sun Microsystems, Inc. business.
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86 * Permission to use, copy, modify, and distribute this
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87 * software is freely granted, provided that this notice
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88 * is preserved.
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89 * ====================================================
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90 */
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91
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92 static const double ln2 = 6.93147180559945286227E-01;
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93 static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
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94 static const double two_pow_p28 = 268435456.0; /* 2**28 */
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95 static const double zero = 0.0;
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96
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97 /* asinh(x)
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98 * Method :
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99 * Based on
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100 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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101 * we have
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102 * asinh(x) := x if 1+x*x=1,
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103 * := sign(x)*(log(x)+ln2)) for large |x|, else
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104 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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105 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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106 */
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107
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108 #ifndef HAVE_ASINH
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109 double
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110 asinh(double x)
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111 {
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112 double w;
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113 double absx = fabs(x);
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114
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115 if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
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116 return x+x;
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117 }
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118 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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119 return x; /* return x inexact except 0 */
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120 }
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121 if (absx > two_pow_p28) { /* |x| > 2**28 */
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122 w = log(absx)+ln2;
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123 }
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124 else if (absx > 2.0) { /* 2 < |x| < 2**28 */
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125 w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
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126 }
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127 else { /* 2**-28 <= |x| < 2= */
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128 double t = x*x;
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129 w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
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130 }
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131 return copysign(w, x);
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132
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133 }
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134 #endif /* HAVE_ASINH */
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135
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136 /* acosh(x)
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137 * Method :
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138 * Based on
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139 * acosh(x) = log [ x + sqrt(x*x-1) ]
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140 * we have
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141 * acosh(x) := log(x)+ln2, if x is large; else
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142 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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143 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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144 *
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145 * Special cases:
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146 * acosh(x) is NaN with signal if x<1.
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147 * acosh(NaN) is NaN without signal.
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148 */
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149
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150 #ifndef HAVE_ACOSH
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151 double
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152 acosh(double x)
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153 {
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154 if (Py_IS_NAN(x)) {
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155 return x+x;
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156 }
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157 if (x < 1.) { /* x < 1; return a signaling NaN */
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158 errno = EDOM;
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159 #ifdef Py_NAN
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160 return Py_NAN;
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161 #else
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162 return (x-x)/(x-x);
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163 #endif
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164 }
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165 else if (x >= two_pow_p28) { /* x > 2**28 */
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166 if (Py_IS_INFINITY(x)) {
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167 return x+x;
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168 } else {
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169 return log(x)+ln2; /* acosh(huge)=log(2x) */
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170 }
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171 }
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172 else if (x == 1.) {
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173 return 0.0; /* acosh(1) = 0 */
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174 }
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175 else if (x > 2.) { /* 2 < x < 2**28 */
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176 double t = x*x;
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177 return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
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178 }
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179 else { /* 1 < x <= 2 */
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180 double t = x - 1.0;
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181 return log1p(t + sqrt(2.0*t + t*t));
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182 }
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183 }
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184 #endif /* HAVE_ACOSH */
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185
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186 /* atanh(x)
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187 * Method :
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188 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
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189 * 2.For x>=0.5
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190 * 1 2x x
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191 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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192 * 2 1 - x 1 - x
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193 *
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194 * For x<0.5
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195 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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196 *
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197 * Special cases:
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198 * atanh(x) is NaN if |x| >= 1 with signal;
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199 * atanh(NaN) is that NaN with no signal;
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200 *
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201 */
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202
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203 #ifndef HAVE_ATANH
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204 double
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205 atanh(double x)
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206 {
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207 double absx;
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208 double t;
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209
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210 if (Py_IS_NAN(x)) {
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211 return x+x;
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212 }
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213 absx = fabs(x);
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214 if (absx >= 1.) { /* |x| >= 1 */
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215 errno = EDOM;
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216 #ifdef Py_NAN
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217 return Py_NAN;
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218 #else
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219 return x/zero;
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220 #endif
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221 }
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222 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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223 return x;
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224 }
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225 if (absx < 0.5) { /* |x| < 0.5 */
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226 t = absx+absx;
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227 t = 0.5 * log1p(t + t*absx / (1.0 - absx));
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228 }
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229 else { /* 0.5 <= |x| <= 1.0 */
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230 t = 0.5 * log1p((absx + absx) / (1.0 - absx));
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231 }
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232 return copysign(t, x);
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233 }
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234 #endif /* HAVE_ATANH */