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annotate src/libm/e_log.c @ 4426:1bceff8f008f

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Fixed bug #943 Ozkan Sezer 2010-02-06 12:31:06 PST Hi: Here are some small fixes for compiling SDL against mingw-w64. (see http://mingw-w64.sourceforge.net/ . Despite the name, it supports both win32 and win64.) src/audio/windx5/directx.h and src/video/windx5/directx.h (both SDL-1.2 and SDL-1.3.) I get compilation errors about some union not having a member named u1 and alike, because of other system headers being included before this one and them already defining DUMMYUNIONNAME and stuff. This header probably assumes that those stuff are defined in windef.h, but mingw-w64 headers define them in _mingw.h. Easily fixed by moving NONAMELESSUNION definition to the top of the file. src/thread/win32/SDL_systhread.c (both SDL-1.2 and SDL-1.3.) : The __GNUC__ case for pfnSDL_CurrentBeginThread is 32-bit centric because _beginthreadex returns uintptr_t, not unsigned long which is 32 bits in win64. Changing the return type to uintptr_t fixes it. video/SDL_blit.h (and configure.in) (SDL-1.3-only) : MinGW-w64 uses msvcrt version of _aligned_malloc and _aligned_free and they are defined in intrin.h (similar to VC). Adding proper ifdefs fixes it. (Notes about macros to check: __MINGW32__ is defined for both mingw.org and for mingw-w64 for both win32 and win64, __MINGW64__ is only defined for _WIN64, so __MINGW64__ can't be used to detect mingw-w64: including _mingw.h and then checking for __MINGW64_VERSION_MAJOR does the trick.) SDL_win32video.h (SDL-1.3-only) : Tweaked the VINWER definition and location in order to avoid multiple redefinition warnings. Hope these are useful. Thanks.
author Sam Lantinga <slouken@libsdl.org>
date Wed, 10 Mar 2010 15:02:58 +0000
parents dc1eb82ffdaa
children
rev   line source
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1 /* @(#)e_log.c 5.1 93/09/24 */
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2 /*
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3 * ====================================================
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4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 *
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6 * Developed at SunPro, a Sun Microsystems, Inc. business.
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7 * Permission to use, copy, modify, and distribute this
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8 * software is freely granted, provided that this notice
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9 * is preserved.
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10 * ====================================================
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11 */
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12
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13 #if defined(LIBM_SCCS) && !defined(lint)
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14 static const char rcsid[] =
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15 "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
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16 #endif
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17
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18 /* __ieee754_log(x)
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19 * Return the logrithm of x
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20 *
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21 * Method :
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22 * 1. Argument Reduction: find k and f such that
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23 * x = 2^k * (1+f),
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24 * where sqrt(2)/2 < 1+f < sqrt(2) .
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25 *
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26 * 2. Approximation of log(1+f).
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27 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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28 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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29 * = 2s + s*R
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30 * We use a special Reme algorithm on [0,0.1716] to generate
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31 * a polynomial of degree 14 to approximate R The maximum error
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32 * of this polynomial approximation is bounded by 2**-58.45. In
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33 * other words,
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34 * 2 4 6 8 10 12 14
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35 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
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36 * (the values of Lg1 to Lg7 are listed in the program)
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37 * and
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38 * | 2 14 | -58.45
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39 * | Lg1*s +...+Lg7*s - R(z) | <= 2
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40 * | |
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41 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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42 * In order to guarantee error in log below 1ulp, we compute log
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43 * by
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44 * log(1+f) = f - s*(f - R) (if f is not too large)
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45 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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46 *
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47 * 3. Finally, log(x) = k*ln2 + log(1+f).
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48 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
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49 * Here ln2 is split into two floating point number:
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50 * ln2_hi + ln2_lo,
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51 * where n*ln2_hi is always exact for |n| < 2000.
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52 *
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53 * Special cases:
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54 * log(x) is NaN with signal if x < 0 (including -INF) ;
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55 * log(+INF) is +INF; log(0) is -INF with signal;
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56 * log(NaN) is that NaN with no signal.
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57 *
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58 * Accuracy:
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59 * according to an error analysis, the error is always less than
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60 * 1 ulp (unit in the last place).
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61 *
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62 * Constants:
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63 * The hexadecimal values are the intended ones for the following
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64 * constants. The decimal values may be used, provided that the
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65 * compiler will convert from decimal to binary accurately enough
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66 * to produce the hexadecimal values shown.
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67 */
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68
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69 #include "math.h"
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70 #include "math_private.h"
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71
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72 #ifdef __STDC__
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73 static const double
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74 #else
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75 static double
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76 #endif
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77 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
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78 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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79 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
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80 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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81 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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82 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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83 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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84 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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85 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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86 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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87
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88 #ifdef __STDC__
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89 static const double zero = 0.0;
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90 #else
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91 static double zero = 0.0;
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92 #endif
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93
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94 #ifdef __STDC__
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95 double attribute_hidden
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96 __ieee754_log(double x)
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97 #else
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98 double attribute_hidden
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99 __ieee754_log(x)
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100 double x;
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101 #endif
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102 {
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103 double hfsq, f, s, z, R, w, t1, t2, dk;
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104 int32_t k, hx, i, j;
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105 u_int32_t lx;
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106
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107 EXTRACT_WORDS(hx, lx, x);
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108
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109 k = 0;
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110 if (hx < 0x00100000) { /* x < 2**-1022 */
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111 if (((hx & 0x7fffffff) | lx) == 0)
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112 return -two54 / zero; /* log(+-0)=-inf */
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113 if (hx < 0)
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114 return (x - x) / zero; /* log(-#) = NaN */
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115 k -= 54;
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116 x *= two54; /* subnormal number, scale up x */
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117 GET_HIGH_WORD(hx, x);
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118 }
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119 if (hx >= 0x7ff00000)
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120 return x + x;
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121 k += (hx >> 20) - 1023;
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122 hx &= 0x000fffff;
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123 i = (hx + 0x95f64) & 0x100000;
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124 SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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125 k += (i >> 20);
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126 f = x - 1.0;
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127 if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
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128 if (f == zero) {
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129 if (k == 0)
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130 return zero;
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131 else {
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132 dk = (double) k;
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133 return dk * ln2_hi + dk * ln2_lo;
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134 }
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135 }
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136 R = f * f * (0.5 - 0.33333333333333333 * f);
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137 if (k == 0)
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138 return f - R;
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139 else {
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140 dk = (double) k;
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141 return dk * ln2_hi - ((R - dk * ln2_lo) - f);
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142 }
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143 }
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144 s = f / (2.0 + f);
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145 dk = (double) k;
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146 z = s * s;
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147 i = hx - 0x6147a;
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148 w = z * z;
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149 j = 0x6b851 - hx;
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150 t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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151 t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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152 i |= j;
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153 R = t2 + t1;
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154 if (i > 0) {
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155 hfsq = 0.5 * f * f;
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156 if (k == 0)
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157 return f - (hfsq - s * (hfsq + R));
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158 else
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159 return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
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160 f);
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161 } else {
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162 if (k == 0)
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163 return f - s * (f - R);
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164 else
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165 return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
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166 }
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167 }