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annotate src/libm/e_log.c @ 2860:6ce28e5287e9

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Date: Sun, 07 Dec 2008 13:35:23 +0100 From: Couriersud Subject: SDL: Mouse last_x, last_y into SDL_Mouse the attached diff moves the static vars last_x and last_y into SDL_Mouse. These, as far as I understand it, should be tied to the individual mouse. The patch also makes the code check for out of window conditions of mouse->x,y when relative movements are passed to MouseSendMotion. Also attached is the latest DirectFB code (dfb20081208) supporting multiple mice and keyboards. This works quite well with sdlmame now. It however needs more testing with different directfb configurations.
author Sam Lantinga <slouken@libsdl.org>
date Mon, 08 Dec 2008 00:52:12 +0000
parents a98604b691c8
children dc1eb82ffdaa
rev   line source
2756
a98604b691c8 Expanded the libm support and put it into a separate directory.
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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 char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
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15 #endif
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16
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17 /* __ieee754_log(x)
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18 * Return the logrithm of x
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19 *
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20 * Method :
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21 * 1. Argument Reduction: find k and f such that
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22 * x = 2^k * (1+f),
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23 * where sqrt(2)/2 < 1+f < sqrt(2) .
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24 *
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25 * 2. Approximation of log(1+f).
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26 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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27 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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28 * = 2s + s*R
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29 * We use a special Reme algorithm on [0,0.1716] to generate
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30 * a polynomial of degree 14 to approximate R The maximum error
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31 * of this polynomial approximation is bounded by 2**-58.45. In
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32 * other words,
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33 * 2 4 6 8 10 12 14
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34 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
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35 * (the values of Lg1 to Lg7 are listed in the program)
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36 * and
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37 * | 2 14 | -58.45
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38 * | Lg1*s +...+Lg7*s - R(z) | <= 2
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39 * | |
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40 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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41 * In order to guarantee error in log below 1ulp, we compute log
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42 * by
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43 * log(1+f) = f - s*(f - R) (if f is not too large)
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44 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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45 *
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46 * 3. Finally, log(x) = k*ln2 + log(1+f).
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47 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
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48 * Here ln2 is split into two floating point number:
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49 * ln2_hi + ln2_lo,
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50 * where n*ln2_hi is always exact for |n| < 2000.
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51 *
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52 * Special cases:
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53 * log(x) is NaN with signal if x < 0 (including -INF) ;
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54 * log(+INF) is +INF; log(0) is -INF with signal;
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55 * log(NaN) is that NaN with no signal.
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56 *
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57 * Accuracy:
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58 * according to an error analysis, the error is always less than
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59 * 1 ulp (unit in the last place).
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60 *
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61 * Constants:
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62 * The hexadecimal values are the intended ones for the following
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63 * constants. The decimal values may be used, provided that the
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64 * compiler will convert from decimal to binary accurately enough
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65 * to produce the hexadecimal values shown.
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66 */
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67
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68 #include "math.h"
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69 #include "math_private.h"
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70
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71 #ifdef __STDC__
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72 static const double
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73 #else
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74 static double
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75 #endif
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76 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
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77 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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78 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
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79 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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80 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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81 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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82 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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83 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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84 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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85 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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86
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87 #ifdef __STDC__
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88 static const double zero = 0.0;
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89 #else
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90 static double zero = 0.0;
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91 #endif
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92
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93 #ifdef __STDC__
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94 double attribute_hidden
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95 __ieee754_log(double x)
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96 #else
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97 double attribute_hidden
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98 __ieee754_log(x)
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99 double x;
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100 #endif
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101 {
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102 double hfsq, f, s, z, R, w, t1, t2, dk;
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103 int32_t k, hx, i, j;
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104 u_int32_t lx;
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105
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106 EXTRACT_WORDS(hx, lx, x);
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107
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108 k = 0;
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109 if (hx < 0x00100000) { /* x < 2**-1022 */
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110 if (((hx & 0x7fffffff) | lx) == 0)
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111 return -two54 / zero; /* log(+-0)=-inf */
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112 if (hx < 0)
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113 return (x - x) / zero; /* log(-#) = NaN */
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114 k -= 54;
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115 x *= two54; /* subnormal number, scale up x */
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116 GET_HIGH_WORD(hx, x);
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117 }
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118 if (hx >= 0x7ff00000)
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119 return x + x;
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120 k += (hx >> 20) - 1023;
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121 hx &= 0x000fffff;
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122 i = (hx + 0x95f64) & 0x100000;
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123 SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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124 k += (i >> 20);
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125 f = x - 1.0;
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126 if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
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127 if (f == zero) {
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128 if (k == 0)
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129 return zero;
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130 else {
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131 dk = (double) k;
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132 return dk * ln2_hi + dk * ln2_lo;
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133 }
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134 }
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135 R = f * f * (0.5 - 0.33333333333333333 * f);
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136 if (k == 0)
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137 return f - R;
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138 else {
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139 dk = (double) k;
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140 return dk * ln2_hi - ((R - dk * ln2_lo) - f);
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141 }
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142 }
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143 s = f / (2.0 + f);
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144 dk = (double) k;
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145 z = s * s;
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146 i = hx - 0x6147a;
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147 w = z * z;
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148 j = 0x6b851 - hx;
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149 t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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150 t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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151 i |= j;
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152 R = t2 + t1;
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153 if (i > 0) {
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154 hfsq = 0.5 * f * f;
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155 if (k == 0)
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156 return f - (hfsq - s * (hfsq + R));
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157 else
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158 return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
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159 f);
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160 } else {
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parents:
diff changeset
161 if (k == 0)
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162 return f - s * (f - R);
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163 else
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164 return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
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parents:
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165 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
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166 }