Mercurial > sdl-ios-xcode
annotate src/video/e_pow.h @ 2670:6e4669f4db49 gsoc2008_nds
Fix for the previous commit: actually 'svn add'ed some files.
author | Darren Alton <dalton@stevens.edu> |
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date | Tue, 10 Jun 2008 06:57:57 +0000 |
parents | c121d94672cb |
children | edd2839b36f7 |
rev | line source |
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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, }, dp_h[] = { |
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71 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ |
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72 |
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73 dp_l[] = { |
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74 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ |
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75 |
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76 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ |
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77 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ |
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78 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ |
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79 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ |
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80 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ |
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81 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ |
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82 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ |
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83 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ |
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84 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ |
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85 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ |
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86 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ |
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87 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ |
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88 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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89 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ |
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90 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ |
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91 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ |
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92 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ |
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93 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ |
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94 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */ |
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95 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ |
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96 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */ |
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97 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */ |
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98 |
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99 #ifdef __STDC__ |
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100 double |
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101 __ieee754_pow(double x, double y) |
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102 #else |
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103 double |
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104 __ieee754_pow(x, y) |
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105 double x, y; |
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106 #endif |
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107 { |
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108 double z, ax, z_h, z_l, p_h, p_l; |
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109 double y1, t1, t2, r, s, t, u, v, w; |
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110 int32_t i, j, k, yisint, n; |
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111 int32_t hx, hy, ix, iy; |
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112 u_int32_t lx, ly; |
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113 |
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114 EXTRACT_WORDS(hx, lx, x); |
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115 EXTRACT_WORDS(hy, ly, y); |
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116 ix = hx & 0x7fffffff; |
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117 iy = hy & 0x7fffffff; |
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118 |
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119 /* y==zero: x**0 = 1 */ |
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120 if ((iy | ly) == 0) |
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121 return one; |
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122 |
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123 /* +-NaN return x+y */ |
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124 if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || |
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125 iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) |
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126 return x + y; |
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127 |
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128 /* determine if y is an odd int when x < 0 |
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129 * yisint = 0 ... y is not an integer |
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130 * yisint = 1 ... y is an odd int |
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131 * yisint = 2 ... y is an even int |
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132 */ |
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133 yisint = 0; |
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134 if (hx < 0) { |
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135 if (iy >= 0x43400000) |
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136 yisint = 2; /* even integer y */ |
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137 else if (iy >= 0x3ff00000) { |
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138 k = (iy >> 20) - 0x3ff; /* exponent */ |
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139 if (k > 20) { |
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140 j = ly >> (52 - k); |
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141 if ((u_int32_t) (j << (52 - k)) == ly) |
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142 yisint = 2 - (j & 1); |
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143 } else if (ly == 0) { |
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144 j = iy >> (20 - k); |
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145 if ((j << (20 - k)) == iy) |
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146 yisint = 2 - (j & 1); |
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147 } |
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148 } |
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149 } |
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150 |
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151 /* special value of y */ |
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152 if (ly == 0) { |
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153 if (iy == 0x7ff00000) { /* y is +-inf */ |
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154 if (((ix - 0x3ff00000) | lx) == 0) |
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155 return y - y; /* inf**+-1 is NaN */ |
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156 else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ |
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157 return (hy >= 0) ? y : zero; |
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158 else /* (|x|<1)**-,+inf = inf,0 */ |
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159 return (hy < 0) ? -y : zero; |
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160 } |
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161 if (iy == 0x3ff00000) { /* y is +-1 */ |
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162 if (hy < 0) |
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163 return one / x; |
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164 else |
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165 return x; |
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166 } |
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167 if (hy == 0x40000000) |
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168 return x * x; /* y is 2 */ |
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169 if (hy == 0x3fe00000) { /* y is 0.5 */ |
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170 if (hx >= 0) /* x >= +0 */ |
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171 return __ieee754_sqrt(x); |
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172 } |
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173 } |
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174 |
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175 ax = x < 0 ? -x : x; /*fabs(x); */ |
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176 /* special value of x */ |
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177 if (lx == 0) { |
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178 if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { |
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179 z = ax; /*x is +-0,+-inf,+-1 */ |
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180 if (hy < 0) |
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181 z = one / z; /* z = (1/|x|) */ |
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182 if (hx < 0) { |
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183 if (((ix - 0x3ff00000) | yisint) == 0) { |
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184 z = (z - z) / (z - z); /* (-1)**non-int is NaN */ |
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185 } else if (yisint == 1) |
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186 z = -z; /* (x<0)**odd = -(|x|**odd) */ |
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187 } |
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188 return z; |
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189 } |
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190 } |
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191 |
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192 /* (x<0)**(non-int) is NaN */ |
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193 if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) |
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194 return (x - x) / (x - x); |
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195 |
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196 /* |y| is huge */ |
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197 if (iy > 0x41e00000) { /* if |y| > 2**31 */ |
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198 if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */ |
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199 if (ix <= 0x3fefffff) |
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200 return (hy < 0) ? huge * huge : tiny * tiny; |
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SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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201 if (ix >= 0x3ff00000) |
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202 return (hy > 0) ? huge * huge : tiny * tiny; |
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SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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203 } |
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SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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204 /* over/underflow if x is not close to one */ |
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SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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205 if (ix < 0x3fefffff) |
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206 return (hy < 0) ? huge * huge : tiny * tiny; |
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SDL 1.2 is moving to a branch, and SDL 1.3 is becoming the head.
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207 if (ix > 0x3ff00000) |
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208 return (hy > 0) ? huge * huge : tiny * tiny; |
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209 /* now |1-x| is tiny <= 2**-20, suffice to compute |
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210 log(x) by x-x^2/2+x^3/3-x^4/4 */ |
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211 t = x - 1; /* t has 20 trailing zeros */ |
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212 w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25)); |
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213 u = ivln2_h * t; /* ivln2_h has 21 sig. bits */ |
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214 v = t * ivln2_l - w * ivln2; |
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215 t1 = u + v; |
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216 SET_LOW_WORD(t1, 0); |
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217 t2 = v - (t1 - u); |
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218 } else { |
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219 double s2, s_h, s_l, t_h, t_l; |
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220 n = 0; |
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221 /* take care subnormal number */ |
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222 if (ix < 0x00100000) { |
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223 ax *= two53; |
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224 n -= 53; |
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225 GET_HIGH_WORD(ix, ax); |
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226 } |
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227 n += ((ix) >> 20) - 0x3ff; |
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228 j = ix & 0x000fffff; |
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229 /* determine interval */ |
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230 ix = j | 0x3ff00000; /* normalize ix */ |
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231 if (j <= 0x3988E) |
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232 k = 0; /* |x|<sqrt(3/2) */ |
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233 else if (j < 0xBB67A) |
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234 k = 1; /* |x|<sqrt(3) */ |
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235 else { |
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236 k = 0; |
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237 n += 1; |
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238 ix -= 0x00100000; |
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239 } |
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240 SET_HIGH_WORD(ax, ix); |
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241 |
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242 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ |
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243 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ |
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244 v = one / (ax + bp[k]); |
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245 s = u * v; |
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246 s_h = s; |
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247 SET_LOW_WORD(s_h, 0); |
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248 /* t_h=ax+bp[k] High */ |
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249 t_h = zero; |
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250 SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)); |
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251 t_l = ax - (t_h - bp[k]); |
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252 s_l = v * ((u - s_h * t_h) - s_h * t_l); |
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253 /* compute log(ax) */ |
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254 s2 = s * s; |
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255 r = s2 * s2 * (L1 + |
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256 s2 * (L2 + |
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257 s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6))))); |
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258 r += s_l * (s_h + s); |
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259 s2 = s_h * s_h; |
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260 t_h = 3.0 + s2 + r; |
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261 SET_LOW_WORD(t_h, 0); |
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262 t_l = r - ((t_h - 3.0) - s2); |
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263 /* u+v = s*(1+...) */ |
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264 u = s_h * t_h; |
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265 v = s_l * t_h + t_l * s; |
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266 /* 2/(3log2)*(s+...) */ |
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267 p_h = u + v; |
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268 SET_LOW_WORD(p_h, 0); |
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269 p_l = v - (p_h - u); |
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270 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ |
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271 z_l = cp_l * p_h + p_l * cp + dp_l[k]; |
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272 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ |
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273 t = (double) n; |
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274 t1 = (((z_h + z_l) + dp_h[k]) + t); |
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275 SET_LOW_WORD(t1, 0); |
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276 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); |
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277 } |
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278 |
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279 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ |
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280 if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) |
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281 s = -one; /* (-ve)**(odd int) */ |
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282 |
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283 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ |
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284 y1 = y; |
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285 SET_LOW_WORD(y1, 0); |
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286 p_l = (y - y1) * t1 + y * t2; |
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287 p_h = y1 * t1; |
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288 z = p_l + p_h; |
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289 EXTRACT_WORDS(j, i, z); |
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290 if (j >= 0x40900000) { /* z >= 1024 */ |
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291 if (((j - 0x40900000) | i) != 0) /* if z > 1024 */ |
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292 return s * huge * huge; /* overflow */ |
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293 else { |
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294 if (p_l + ovt > z - p_h) |
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295 return s * huge * huge; /* overflow */ |
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296 } |
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297 } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */ |
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298 if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */ |
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299 return s * tiny * tiny; /* underflow */ |
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300 else { |
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301 if (p_l <= z - p_h) |
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302 return s * tiny * tiny; /* underflow */ |
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303 } |
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304 } |
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305 /* |
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306 * compute 2**(p_h+p_l) |
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307 */ |
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308 i = j & 0x7fffffff; |
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309 k = (i >> 20) - 0x3ff; |
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310 n = 0; |
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311 if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ |
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312 n = j + (0x00100000 >> (k + 1)); |
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313 k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */ |
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314 t = zero; |
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315 SET_HIGH_WORD(t, n & ~(0x000fffff >> k)); |
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316 n = ((n & 0x000fffff) | 0x00100000) >> (20 - k); |
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317 if (j < 0) |
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318 n = -n; |
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319 p_h -= t; |
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320 } |
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321 t = p_l + p_h; |
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322 SET_LOW_WORD(t, 0); |
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323 u = t * lg2_h; |
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324 v = (p_l - (t - p_h)) * lg2 + t * lg2_l; |
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325 z = u + v; |
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326 w = v - (z - u); |
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327 t = z * z; |
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328 t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); |
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329 r = (z * t1) / (t1 - two) - (w + z * w); |
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330 z = one - (r - z); |
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331 GET_HIGH_WORD(j, z); |
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332 j += (n << 20); |
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333 if ((j >> 20) <= 0) |
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334 z = SDL_NAME(scalbn) (z, n); /* subnormal output */ |
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335 else |
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336 SET_HIGH_WORD(z, j); |
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337 return s * z; |
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338 } |
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339 |
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340 /* vi: set ts=4 sw=4 expandtab: */ |