Mercurial > cpython-lru_cache-weakref

annotate Python/pymath.c @ 58689:514b56efd89a 3.1

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Merged revisions 77962 via svnmerge from svn+ssh://pythondev@svn.python.org/python/branches/py3k ................ r77962 | r.david.murray | 2010-02-04 11:41:57 -0500 (Thu, 04 Feb 2010) | 17 lines Merged revisions 77943,77959-77960 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r77943 | r.david.murray | 2010-02-03 08:36:23 -0500 (Wed, 03 Feb 2010) | 2 lines Explicitly mention the default value for formatdate's usegmt parameter. ........ r77959 | nick.coghlan | 2010-02-04 07:43:58 -0500 (Thu, 04 Feb 2010) | 1 line Issue 6760: Clarify args handling for subprocess.Popen. Patch by Chris Rebert ........ r77960 | r.david.murray | 2010-02-04 11:33:31 -0500 (Thu, 04 Feb 2010) | 2 lines Add Chris Rebert to ACKS for issue 6760 Popen doc improvements. ........ ................
author R. David Murray <rdmurray@bitdance.com>
date Thu, 04 Feb 2010 16:44:31 +0000
parents 28645a961004
children f197407bdba2 9751ddcc1882
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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 #ifdef HAVE_GCC_ASM_FOR_X87
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17
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18 /* inline assembly for getting and setting the 387 FPU control word on
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19 gcc/x86 */
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20
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21 unsigned short _Py_get_387controlword(void) {
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22 unsigned short cw;
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23 __asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
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24 return cw;
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25 }
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26
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27 void _Py_set_387controlword(unsigned short cw) {
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28 __asm__ __volatile__ ("fldcw %0" : : "m" (cw));
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29 }
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30
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31 #endif
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32
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33
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34 #ifndef HAVE_HYPOT
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35 double hypot(double x, double y)
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36 {
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37 double yx;
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38
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39 x = fabs(x);
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40 y = fabs(y);
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41 if (x < y) {
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42 double temp = x;
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43 x = y;
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44 y = temp;
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45 }
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46 if (x == 0.)
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47 return 0.;
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48 else {
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49 yx = y/x;
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50 return x*sqrt(1.+yx*yx);
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51 }
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52 }
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53 #endif /* HAVE_HYPOT */
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54
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55 #ifndef HAVE_COPYSIGN
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56 double
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57 copysign(double x, double y)
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58 {
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59 /* use atan2 to distinguish -0. from 0. */
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60 if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) {
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61 return fabs(x);
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62 } else {
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63 return -fabs(x);
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64 }
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65 }
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66 #endif /* HAVE_COPYSIGN */
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67
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68 #ifndef HAVE_ROUND
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69 double
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70 round(double x)
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71 {
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72 double absx, y;
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73 absx = fabs(x);
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74 y = floor(absx);
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75 if (absx - y >= 0.5)
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76 y += 1.0;
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77 return copysign(y, x);
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78 }
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79 #endif /* HAVE_ROUND */
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80
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81 #ifndef HAVE_LOG1P
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82 #include <float.h>
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83
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84 double
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85 log1p(double x)
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86 {
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87 /* For x small, we use the following approach. Let y be the nearest
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88 float to 1+x, then
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89
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90 1+x = y * (1 - (y-1-x)/y)
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91
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92 so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,
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93 the second term is well approximated by (y-1-x)/y. If abs(x) >=
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94 DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
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95 then y-1-x will be exactly representable, and is computed exactly
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96 by (y-1)-x.
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97
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98 If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
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99 round-to-nearest then this method is slightly dangerous: 1+x could
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100 be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
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101 case y-1-x will not be exactly representable any more and the
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102 result can be off by many ulps. But this is easily fixed: for a
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103 floating-point number |x| < DBL_EPSILON/2., the closest
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104 floating-point number to log(1+x) is exactly x.
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105 */
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106
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107 double y;
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108 if (fabs(x) < DBL_EPSILON/2.) {
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109 return x;
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110 } else if (-0.5 <= x && x <= 1.) {
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111 /* WARNING: it's possible than an overeager compiler
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112 will incorrectly optimize the following two lines
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113 to the equivalent of "return log(1.+x)". If this
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114 happens, then results from log1p will be inaccurate
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115 for small x. */
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116 y = 1.+x;
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117 return log(y)-((y-1.)-x)/y;
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118 } else {
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119 /* NaNs and infinities should end up here */
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120 return log(1.+x);
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121 }
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122 }
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123 #endif /* HAVE_LOG1P */
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124
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125 /*
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126 * ====================================================
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127 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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128 *
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129 * Developed at SunPro, a Sun Microsystems, Inc. business.
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130 * Permission to use, copy, modify, and distribute this
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131 * software is freely granted, provided that this notice
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132 * is preserved.
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133 * ====================================================
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134 */
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135
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136 static const double ln2 = 6.93147180559945286227E-01;
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137 static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
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138 static const double two_pow_p28 = 268435456.0; /* 2**28 */
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139 static const double zero = 0.0;
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140
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141 /* asinh(x)
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142 * Method :
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143 * Based on
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144 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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145 * we have
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146 * asinh(x) := x if 1+x*x=1,
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147 * := sign(x)*(log(x)+ln2)) for large |x|, else
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148 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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149 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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150 */
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151
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152 #ifndef HAVE_ASINH
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153 double
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154 asinh(double x)
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155 {
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156 double w;
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157 double absx = fabs(x);
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158
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159 if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
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160 return x+x;
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161 }
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162 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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163 return x; /* return x inexact except 0 */
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164 }
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165 if (absx > two_pow_p28) { /* |x| > 2**28 */
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166 w = log(absx)+ln2;
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167 }
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168 else if (absx > 2.0) { /* 2 < |x| < 2**28 */
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169 w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
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170 }
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171 else { /* 2**-28 <= |x| < 2= */
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172 double t = x*x;
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173 w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
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174 }
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175 return copysign(w, x);
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176
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177 }
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178 #endif /* HAVE_ASINH */
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179
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180 /* acosh(x)
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181 * Method :
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182 * Based on
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183 * acosh(x) = log [ x + sqrt(x*x-1) ]
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184 * we have
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185 * acosh(x) := log(x)+ln2, if x is large; else
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186 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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187 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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188 *
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189 * Special cases:
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190 * acosh(x) is NaN with signal if x<1.
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191 * acosh(NaN) is NaN without signal.
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192 */
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193
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194 #ifndef HAVE_ACOSH
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195 double
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196 acosh(double x)
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197 {
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198 if (Py_IS_NAN(x)) {
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199 return x+x;
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200 }
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201 if (x < 1.) { /* x < 1; return a signaling NaN */
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202 errno = EDOM;
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203 #ifdef Py_NAN
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204 return Py_NAN;
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205 #else
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206 return (x-x)/(x-x);
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207 #endif
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208 }
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209 else if (x >= two_pow_p28) { /* x > 2**28 */
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210 if (Py_IS_INFINITY(x)) {
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211 return x+x;
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212 } else {
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213 return log(x)+ln2; /* acosh(huge)=log(2x) */
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214 }
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215 }
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216 else if (x == 1.) {
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217 return 0.0; /* acosh(1) = 0 */
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218 }
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219 else if (x > 2.) { /* 2 < x < 2**28 */
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220 double t = x*x;
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221 return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
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222 }
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223 else { /* 1 < x <= 2 */
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224 double t = x - 1.0;
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225 return log1p(t + sqrt(2.0*t + t*t));
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226 }
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227 }
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228 #endif /* HAVE_ACOSH */
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229
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230 /* atanh(x)
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231 * Method :
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232 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
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233 * 2.For x>=0.5
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234 * 1 2x x
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235 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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236 * 2 1 - x 1 - x
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237 *
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238 * For x<0.5
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239 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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240 *
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241 * Special cases:
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242 * atanh(x) is NaN if |x| >= 1 with signal;
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243 * atanh(NaN) is that NaN with no signal;
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244 *
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245 */
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246
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247 #ifndef HAVE_ATANH
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248 double
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249 atanh(double x)
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250 {
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251 double absx;
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252 double t;
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253
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254 if (Py_IS_NAN(x)) {
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255 return x+x;
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256 }
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257 absx = fabs(x);
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258 if (absx >= 1.) { /* |x| >= 1 */
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259 errno = EDOM;
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260 #ifdef Py_NAN
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261 return Py_NAN;
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262 #else
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263 return x/zero;
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264 #endif
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265 }
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266 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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267 return x;
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268 }
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269 if (absx < 0.5) { /* |x| < 0.5 */
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270 t = absx+absx;
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271 t = 0.5 * log1p(t + t*absx / (1.0 - absx));
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272 }
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273 else { /* 0.5 <= |x| <= 1.0 */
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274 t = 0.5 * log1p((absx + absx) / (1.0 - absx));
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275 }
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276 return copysign(t, x);
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277 }
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278 #endif /* HAVE_ATANH */