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annotate src/video/e_log.h @ 2349:0381047f2210 gsoc2008_iphone

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The class SDL_uikitappdelegate acts as the UIApplicationDelegate for an iPhone SDL project. This class is reponsible for application control flow, including initial setup of working directory, forwarding command line arguments to the user's main function, and handling application termination.
author Holmes Futrell <hfutrell@umail.ucsb.edu>
date Thu, 17 Jul 2008 22:29:37 +0000
parents c121d94672cb
children
rev   line source
1330
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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 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
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79 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
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80 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
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81 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
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82 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
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83 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
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84 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
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85
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86 #ifdef __STDC__
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87 double
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88 __ieee754_log(double x)
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89 #else
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90 double
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91 __ieee754_log(x)
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92 double x;
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93 #endif
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94 {
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95 double hfsq, f, s, z, R, w, t1, t2, dk;
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96 int32_t k, hx, i, j;
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97 u_int32_t lx;
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98
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99 EXTRACT_WORDS(hx, lx, x);
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100
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101 k = 0;
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102 if (hx < 0x00100000) { /* x < 2**-1022 */
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103 if (((hx & 0x7fffffff) | lx) == 0)
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104 return -two54 / zero; /* log(+-0)=-inf */
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105 if (hx < 0)
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106 return (x - x) / zero; /* log(-#) = NaN */
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107 k -= 54;
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108 x *= two54; /* subnormal number, scale up x */
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109 GET_HIGH_WORD(hx, x);
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110 }
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111 if (hx >= 0x7ff00000)
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112 return x + x;
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113 k += (hx >> 20) - 1023;
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114 hx &= 0x000fffff;
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115 i = (hx + 0x95f64) & 0x100000;
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116 SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */
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117 k += (i >> 20);
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118 f = x - 1.0;
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119 if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */
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120 if (f == zero) {
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121 if (k == 0)
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122 return zero;
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123 else {
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124 dk = (double) k;
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125 return dk * ln2_hi + dk * ln2_lo;
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126 }
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127 }
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128 R = f * f * (0.5 - 0.33333333333333333 * f);
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129 if (k == 0)
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130 return f - R;
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131 else {
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132 dk = (double) k;
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133 return dk * ln2_hi - ((R - dk * ln2_lo) - f);
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134 }
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135 }
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136 s = f / (2.0 + f);
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137 dk = (double) k;
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138 z = s * s;
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139 i = hx - 0x6147a;
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140 w = z * z;
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141 j = 0x6b851 - hx;
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142 t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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143 t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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144 i |= j;
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145 R = t2 + t1;
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146 if (i > 0) {
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147 hfsq = 0.5 * f * f;
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148 if (k == 0)
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149 return f - (hfsq - s * (hfsq + R));
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150 else
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151 return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
c121d94672cb SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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152 f);
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153 } else {
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diff changeset
154 if (k == 0)
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155 return f - s * (f - R);
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156 else
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157 return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
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158 }
1330
450721ad5436 It's now possible to build SDL without any C runtime at all on Windows,
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parents:
diff changeset
159 }
1895
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160
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161 /* vi: set ts=4 sw=4 expandtab: */