Mercurial > sdl-ios-xcode
annotate src/video/e_pow.h @ 3958:85b6fb6a5e3c SDL-1.2
Actually, this is a better fix...clear the error state once if everything we
need loaded; it's more efficient, and works even if the last unnecessary
xrandr symbol failed to load. Otherwise, leave the original loadso error, so
the end user can find out what symbol failed.
author | Ryan C. Gordon <icculus@icculus.org> |
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date | Wed, 13 Jun 2007 08:00:10 +0000 |
parents | 7a610f25c12f |
children | 782fd950bd46 c121d94672cb |
rev | line source |
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It's now possible to build SDL without any C runtime at all on Windows,
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1 /* @(#)e_pow.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_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; |
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15 #endif |
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16 |
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17 /* __ieee754_pow(x,y) return x**y |
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18 * |
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19 * n |
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20 * Method: Let x = 2 * (1+f) |
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21 * 1. Compute and return log2(x) in two pieces: |
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22 * log2(x) = w1 + w2, |
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23 * where w1 has 53-24 = 29 bit trailing zeros. |
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24 * 2. Perform y*log2(x) = n+y' by simulating muti-precision |
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25 * arithmetic, where |y'|<=0.5. |
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26 * 3. Return x**y = 2**n*exp(y'*log2) |
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27 * |
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28 * Special cases: |
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29 * 1. (anything) ** 0 is 1 |
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30 * 2. (anything) ** 1 is itself |
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31 * 3. (anything) ** NAN is NAN |
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32 * 4. NAN ** (anything except 0) is NAN |
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33 * 5. +-(|x| > 1) ** +INF is +INF |
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34 * 6. +-(|x| > 1) ** -INF is +0 |
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35 * 7. +-(|x| < 1) ** +INF is +0 |
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36 * 8. +-(|x| < 1) ** -INF is +INF |
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37 * 9. +-1 ** +-INF is NAN |
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38 * 10. +0 ** (+anything except 0, NAN) is +0 |
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39 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 |
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40 * 12. +0 ** (-anything except 0, NAN) is +INF |
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41 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF |
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42 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) |
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43 * 15. +INF ** (+anything except 0,NAN) is +INF |
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44 * 16. +INF ** (-anything except 0,NAN) is +0 |
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45 * 17. -INF ** (anything) = -0 ** (-anything) |
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46 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) |
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47 * 19. (-anything except 0 and inf) ** (non-integer) is NAN |
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48 * |
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49 * Accuracy: |
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50 * pow(x,y) returns x**y nearly rounded. In particular |
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51 * pow(integer,integer) |
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52 * always returns the correct integer provided it is |
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53 * representable. |
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54 * |
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55 * Constants : |
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56 * The hexadecimal values are the intended ones for the following |
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57 * constants. The decimal values may be used, provided that the |
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58 * compiler will convert from decimal to binary accurately enough |
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59 * to produce the hexadecimal values shown. |
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60 */ |
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61 |
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62 /*#include "math.h"*/ |
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63 #include "math_private.h" |
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64 |
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65 #ifdef __STDC__ |
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66 static const double |
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67 #else |
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68 static double |
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69 #endif |
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70 bp[] = {1.0, 1.5,}, |
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71 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ |
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72 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ |
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73 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ |
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74 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ |
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75 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ |
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76 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ |
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77 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ |
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78 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ |
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79 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ |
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80 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ |
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81 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ |
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82 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ |
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83 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ |
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84 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ |
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85 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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86 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ |
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87 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ |
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88 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ |
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89 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ |
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90 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ |
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91 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ |
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92 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ |
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93 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ |
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94 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ |
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95 |
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96 #ifdef __STDC__ |
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97 double __ieee754_pow(double x, double y) |
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98 #else |
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99 double __ieee754_pow(x,y) |
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100 double x, y; |
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101 #endif |
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102 { |
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103 double z,ax,z_h,z_l,p_h,p_l; |
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104 double y1,t1,t2,r,s,t,u,v,w; |
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105 int32_t i,j,k,yisint,n; |
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106 int32_t hx,hy,ix,iy; |
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107 u_int32_t lx,ly; |
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108 |
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109 EXTRACT_WORDS(hx,lx,x); |
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110 EXTRACT_WORDS(hy,ly,y); |
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111 ix = hx&0x7fffffff; iy = hy&0x7fffffff; |
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112 |
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113 /* y==zero: x**0 = 1 */ |
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114 if((iy|ly)==0) return one; |
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115 |
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116 /* +-NaN return x+y */ |
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117 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || |
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118 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) |
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119 return x+y; |
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120 |
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121 /* determine if y is an odd int when x < 0 |
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122 * yisint = 0 ... y is not an integer |
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123 * yisint = 1 ... y is an odd int |
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124 * yisint = 2 ... y is an even int |
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125 */ |
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126 yisint = 0; |
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127 if(hx<0) { |
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128 if(iy>=0x43400000) yisint = 2; /* even integer y */ |
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129 else if(iy>=0x3ff00000) { |
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130 k = (iy>>20)-0x3ff; /* exponent */ |
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131 if(k>20) { |
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132 j = ly>>(52-k); |
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133 if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1); |
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134 } else if(ly==0) { |
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135 j = iy>>(20-k); |
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136 if((j<<(20-k))==iy) yisint = 2-(j&1); |
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137 } |
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138 } |
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139 } |
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140 |
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141 /* special value of y */ |
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142 if(ly==0) { |
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143 if (iy==0x7ff00000) { /* y is +-inf */ |
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144 if(((ix-0x3ff00000)|lx)==0) |
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145 return y - y; /* inf**+-1 is NaN */ |
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146 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ |
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147 return (hy>=0)? y: zero; |
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148 else /* (|x|<1)**-,+inf = inf,0 */ |
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149 return (hy<0)?-y: zero; |
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150 } |
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151 if(iy==0x3ff00000) { /* y is +-1 */ |
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152 if(hy<0) return one/x; else return x; |
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153 } |
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154 if(hy==0x40000000) return x*x; /* y is 2 */ |
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155 if(hy==0x3fe00000) { /* y is 0.5 */ |
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156 if(hx>=0) /* x >= +0 */ |
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157 return __ieee754_sqrt(x); |
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158 } |
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159 } |
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160 |
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161 ax = x < 0 ? -x : x; /*fabs(x);*/ |
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162 /* special value of x */ |
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163 if(lx==0) { |
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164 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ |
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165 z = ax; /*x is +-0,+-inf,+-1*/ |
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166 if(hy<0) z = one/z; /* z = (1/|x|) */ |
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167 if(hx<0) { |
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168 if(((ix-0x3ff00000)|yisint)==0) { |
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169 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
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170 } else if(yisint==1) |
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171 z = -z; /* (x<0)**odd = -(|x|**odd) */ |
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172 } |
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173 return z; |
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174 } |
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175 } |
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176 |
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177 /* (x<0)**(non-int) is NaN */ |
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178 if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); |
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179 |
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180 /* |y| is huge */ |
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181 if(iy>0x41e00000) { /* if |y| > 2**31 */ |
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182 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ |
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183 if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; |
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184 if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; |
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185 } |
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186 /* over/underflow if x is not close to one */ |
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187 if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; |
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188 if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; |
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189 /* now |1-x| is tiny <= 2**-20, suffice to compute |
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190 log(x) by x-x^2/2+x^3/3-x^4/4 */ |
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191 t = x-1; /* t has 20 trailing zeros */ |
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192 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); |
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193 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ |
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194 v = t*ivln2_l-w*ivln2; |
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195 t1 = u+v; |
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196 SET_LOW_WORD(t1,0); |
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197 t2 = v-(t1-u); |
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198 } else { |
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199 double s2,s_h,s_l,t_h,t_l; |
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200 n = 0; |
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201 /* take care subnormal number */ |
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202 if(ix<0x00100000) |
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203 {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } |
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204 n += ((ix)>>20)-0x3ff; |
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205 j = ix&0x000fffff; |
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206 /* determine interval */ |
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207 ix = j|0x3ff00000; /* normalize ix */ |
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208 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ |
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209 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ |
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210 else {k=0;n+=1;ix -= 0x00100000;} |
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211 SET_HIGH_WORD(ax,ix); |
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212 |
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213 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ |
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214 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ |
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215 v = one/(ax+bp[k]); |
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216 s = u*v; |
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217 s_h = s; |
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218 SET_LOW_WORD(s_h,0); |
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219 /* t_h=ax+bp[k] High */ |
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220 t_h = zero; |
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221 SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); |
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222 t_l = ax - (t_h-bp[k]); |
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223 s_l = v*((u-s_h*t_h)-s_h*t_l); |
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224 /* compute log(ax) */ |
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225 s2 = s*s; |
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226 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); |
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227 r += s_l*(s_h+s); |
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228 s2 = s_h*s_h; |
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229 t_h = 3.0+s2+r; |
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230 SET_LOW_WORD(t_h,0); |
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231 t_l = r-((t_h-3.0)-s2); |
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232 /* u+v = s*(1+...) */ |
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233 u = s_h*t_h; |
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234 v = s_l*t_h+t_l*s; |
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235 /* 2/(3log2)*(s+...) */ |
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236 p_h = u+v; |
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237 SET_LOW_WORD(p_h,0); |
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238 p_l = v-(p_h-u); |
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239 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ |
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240 z_l = cp_l*p_h+p_l*cp+dp_l[k]; |
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241 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ |
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242 t = (double)n; |
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243 t1 = (((z_h+z_l)+dp_h[k])+t); |
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244 SET_LOW_WORD(t1,0); |
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245 t2 = z_l-(((t1-t)-dp_h[k])-z_h); |
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246 } |
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247 |
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248 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ |
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249 if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) |
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250 s = -one;/* (-ve)**(odd int) */ |
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251 |
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252 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ |
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253 y1 = y; |
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254 SET_LOW_WORD(y1,0); |
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255 p_l = (y-y1)*t1+y*t2; |
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256 p_h = y1*t1; |
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257 z = p_l+p_h; |
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258 EXTRACT_WORDS(j,i,z); |
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259 if (j>=0x40900000) { /* z >= 1024 */ |
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260 if(((j-0x40900000)|i)!=0) /* if z > 1024 */ |
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261 return s*huge*huge; /* overflow */ |
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262 else { |
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263 if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ |
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264 } |
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265 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ |
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266 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ |
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267 return s*tiny*tiny; /* underflow */ |
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268 else { |
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269 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ |
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270 } |
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271 } |
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272 /* |
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273 * compute 2**(p_h+p_l) |
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274 */ |
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275 i = j&0x7fffffff; |
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276 k = (i>>20)-0x3ff; |
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277 n = 0; |
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278 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ |
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279 n = j+(0x00100000>>(k+1)); |
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280 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ |
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281 t = zero; |
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282 SET_HIGH_WORD(t,n&~(0x000fffff>>k)); |
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283 n = ((n&0x000fffff)|0x00100000)>>(20-k); |
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284 if(j<0) n = -n; |
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285 p_h -= t; |
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286 } |
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287 t = p_l+p_h; |
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288 SET_LOW_WORD(t,0); |
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289 u = t*lg2_h; |
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290 v = (p_l-(t-p_h))*lg2+t*lg2_l; |
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291 z = u+v; |
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292 w = v-(z-u); |
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293 t = z*z; |
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294 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); |
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295 r = (z*t1)/(t1-two)-(w+z*w); |
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296 z = one-(r-z); |
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297 GET_HIGH_WORD(j,z); |
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298 j += (n<<20); |
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299 if((j>>20)<=0) z = SDL_NAME(scalbn)(z,n); /* subnormal output */ |
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300 else SET_HIGH_WORD(z,j); |
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301 return s*z; |
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302 } |