Mercurial > cpython-lru_cache-weakref

annotate Python/pymath.c @ 53207:fe99a562b708

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Silence compiler warnings on VS8.0
author Mark Dickinson <dickinsm@gmail.com>
date Fri, 17 Apr 2009 19:29:46 +0000
parents 97ae7a709c1d
children c5c8680ee0b1
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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 USING_X87_FPU
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17 # ifdef HAVE_GCC_ASM_FOR_X87
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18
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19 /* inline assembly for getting and setting the 387 FPU control word on
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20 gcc/x86 */
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21
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22 unsigned short _Py_get_387controlword(void) {
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23 unsigned short cw;
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24 __asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
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25 return cw;
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26 }
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27
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28 void _Py_set_387controlword(unsigned short cw) {
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29 __asm__ __volatile__ ("fldcw %0" : : "m" (cw));
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30 }
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31
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32 # else
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33 # error "Unable to get and set x87 control word"
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34 # endif
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35 #endif
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36
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37
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38 #ifndef HAVE_HYPOT
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39 double hypot(double x, double y)
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40 {
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41 double yx;
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42
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43 x = fabs(x);
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44 y = fabs(y);
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45 if (x < y) {
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46 double temp = x;
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47 x = y;
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48 y = temp;
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49 }
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50 if (x == 0.)
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51 return 0.;
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52 else {
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53 yx = y/x;
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54 return x*sqrt(1.+yx*yx);
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55 }
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56 }
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57 #endif /* HAVE_HYPOT */
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58
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59 #ifndef HAVE_COPYSIGN
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60 static double
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61 copysign(double x, double y)
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62 {
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63 /* use atan2 to distinguish -0. from 0. */
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64 if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) {
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65 return fabs(x);
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66 } else {
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67 return -fabs(x);
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68 }
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69 }
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70 #endif /* HAVE_COPYSIGN */
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71
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72 #ifndef HAVE_LOG1P
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73 #include <float.h>
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74
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75 double
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76 log1p(double x)
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77 {
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78 /* For x small, we use the following approach. Let y be the nearest
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79 float to 1+x, then
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80
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81 1+x = y * (1 - (y-1-x)/y)
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82
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83 so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,
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84 the second term is well approximated by (y-1-x)/y. If abs(x) >=
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85 DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
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86 then y-1-x will be exactly representable, and is computed exactly
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87 by (y-1)-x.
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88
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89 If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
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90 round-to-nearest then this method is slightly dangerous: 1+x could
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91 be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
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92 case y-1-x will not be exactly representable any more and the
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93 result can be off by many ulps. But this is easily fixed: for a
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94 floating-point number |x| < DBL_EPSILON/2., the closest
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95 floating-point number to log(1+x) is exactly x.
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96 */
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97
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98 double y;
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99 if (fabs(x) < DBL_EPSILON/2.) {
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100 return x;
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101 } else if (-0.5 <= x && x <= 1.) {
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102 /* WARNING: it's possible than an overeager compiler
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103 will incorrectly optimize the following two lines
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104 to the equivalent of "return log(1.+x)". If this
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105 happens, then results from log1p will be inaccurate
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106 for small x. */
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107 y = 1.+x;
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108 return log(y)-((y-1.)-x)/y;
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109 } else {
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110 /* NaNs and infinities should end up here */
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111 return log(1.+x);
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112 }
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113 }
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114 #endif /* HAVE_LOG1P */
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115
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116 /*
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117 * ====================================================
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118 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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119 *
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120 * Developed at SunPro, a Sun Microsystems, Inc. business.
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121 * Permission to use, copy, modify, and distribute this
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122 * software is freely granted, provided that this notice
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123 * is preserved.
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124 * ====================================================
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125 */
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126
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127 static const double ln2 = 6.93147180559945286227E-01;
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128 static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
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129 static const double two_pow_p28 = 268435456.0; /* 2**28 */
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130 static const double zero = 0.0;
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131
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132 /* asinh(x)
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133 * Method :
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134 * Based on
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135 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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136 * we have
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137 * asinh(x) := x if 1+x*x=1,
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138 * := sign(x)*(log(x)+ln2)) for large |x|, else
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139 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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140 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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141 */
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142
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143 #ifndef HAVE_ASINH
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144 double
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145 asinh(double x)
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146 {
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147 double w;
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148 double absx = fabs(x);
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149
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150 if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
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151 return x+x;
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152 }
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153 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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154 return x; /* return x inexact except 0 */
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155 }
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156 if (absx > two_pow_p28) { /* |x| > 2**28 */
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157 w = log(absx)+ln2;
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158 }
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159 else if (absx > 2.0) { /* 2 < |x| < 2**28 */
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160 w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
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161 }
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162 else { /* 2**-28 <= |x| < 2= */
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163 double t = x*x;
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164 w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
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165 }
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166 return copysign(w, x);
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167
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168 }
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169 #endif /* HAVE_ASINH */
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170
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171 /* acosh(x)
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172 * Method :
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173 * Based on
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174 * acosh(x) = log [ x + sqrt(x*x-1) ]
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175 * we have
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176 * acosh(x) := log(x)+ln2, if x is large; else
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177 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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178 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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179 *
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180 * Special cases:
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181 * acosh(x) is NaN with signal if x<1.
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182 * acosh(NaN) is NaN without signal.
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183 */
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184
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185 #ifndef HAVE_ACOSH
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186 double
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187 acosh(double x)
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188 {
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189 if (Py_IS_NAN(x)) {
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190 return x+x;
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191 }
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192 if (x < 1.) { /* x < 1; return a signaling NaN */
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193 errno = EDOM;
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194 #ifdef Py_NAN
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195 return Py_NAN;
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196 #else
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197 return (x-x)/(x-x);
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198 #endif
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199 }
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200 else if (x >= two_pow_p28) { /* x > 2**28 */
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201 if (Py_IS_INFINITY(x)) {
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202 return x+x;
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203 } else {
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204 return log(x)+ln2; /* acosh(huge)=log(2x) */
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205 }
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206 }
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207 else if (x == 1.) {
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208 return 0.0; /* acosh(1) = 0 */
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209 }
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210 else if (x > 2.) { /* 2 < x < 2**28 */
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211 double t = x*x;
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212 return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
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213 }
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214 else { /* 1 < x <= 2 */
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215 double t = x - 1.0;
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216 return log1p(t + sqrt(2.0*t + t*t));
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217 }
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218 }
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219 #endif /* HAVE_ACOSH */
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220
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221 /* atanh(x)
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222 * Method :
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223 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
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224 * 2.For x>=0.5
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225 * 1 2x x
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226 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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227 * 2 1 - x 1 - x
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228 *
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229 * For x<0.5
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230 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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231 *
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232 * Special cases:
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233 * atanh(x) is NaN if |x| >= 1 with signal;
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234 * atanh(NaN) is that NaN with no signal;
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235 *
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236 */
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237
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238 #ifndef HAVE_ATANH
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239 double
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240 atanh(double x)
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241 {
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242 double absx;
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243 double t;
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244
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245 if (Py_IS_NAN(x)) {
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246 return x+x;
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247 }
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248 absx = fabs(x);
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249 if (absx >= 1.) { /* |x| >= 1 */
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250 errno = EDOM;
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251 #ifdef Py_NAN
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252 return Py_NAN;
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253 #else
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254 return x/zero;
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255 #endif
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256 }
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257 if (absx < two_pow_m28) { /* |x| < 2**-28 */
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258 return x;
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259 }
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260 if (absx < 0.5) { /* |x| < 0.5 */
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261 t = absx+absx;
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262 t = 0.5 * log1p(t + t*absx / (1.0 - absx));
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263 }
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264 else { /* 0.5 <= |x| <= 1.0 */
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265 t = 0.5 * log1p((absx + absx) / (1.0 - absx));
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266 }
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267 return copysign(t, x);
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268 }
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269 #endif /* HAVE_ATANH */