1 | // |
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2 | // Lol Engine |
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3 | // |
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4 | // Copyright: (c) 2010-2011 Sam Hocevar <sam@hocevar.net> |
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5 | // This program is free software; you can redistribute it and/or |
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6 | // modify it under the terms of the Do What The Fuck You Want To |
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7 | // Public License, Version 2, as published by Sam Hocevar. See |
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8 | // http://sam.zoy.org/projects/COPYING.WTFPL for more details. |
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9 | // |
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10 | |
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11 | #if defined HAVE_CONFIG_H |
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12 | # include "config.h" |
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13 | #endif |
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14 | |
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15 | #include "core.h" |
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16 | |
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17 | using namespace std; |
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18 | |
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19 | namespace lol |
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20 | { |
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21 | |
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22 | /* Lookup table-based algorithm from “Fast Half Float Conversions” |
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23 | * by Jeroen van der Zijp, November 2008. No rounding is performed, |
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24 | * and some NaN values may be incorrectly converted to Inf. */ |
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25 | half half::makefast(float f) |
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26 | { |
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27 | #define S4(x) S1(4*(x)), S1(4*(x)+1), S1(4*(x)+2), S1(4*(x)+3) |
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28 | #define S16(x) S4(4*(x)), S4(4*(x)+1), S4(4*(x)+2), S4(4*(x)+3) |
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29 | #define S64(x) S16(4*(x)), S16(4*(x)+1), S16(4*(x)+2), S16(4*(x)+3) |
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30 | #define S256(x) S64(4*(x)), S64(4*(x)+1), S64(4*(x)+2), S64(4*(x)+3) |
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31 | |
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32 | static uint16_t const basetable[512] = |
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33 | { |
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34 | #define S1(i) (((i) < 103) ? 0x0000: \ |
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35 | ((i) < 113) ? 0x0400 >> (113 - (i)) : \ |
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36 | ((i) < 143) ? ((i) - 112) << 10 : 0x7c00) |
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37 | S256(0), |
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38 | #undef S1 |
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39 | #define S1(i) (0x8000 | (((i) < 103) ? 0x0000 : \ |
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40 | ((i) < 113) ? 0x0400 >> (113 - (i)): \ |
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41 | ((i) < 143) ? ((i) - 112) << 10 : 0x7c00)) |
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42 | S256(0), |
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43 | #undef S1 |
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44 | }; |
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45 | |
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46 | static uint8_t const shifttable[512] = |
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47 | { |
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48 | #define S1(i) (((i) < 103) ? 24 : \ |
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49 | ((i) < 113) ? 126 - (i) : \ |
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50 | ((i) < 143 || (i) == 255) ? 13 : 24) |
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51 | S256(0), S256(0), |
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52 | #undef S1 |
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53 | }; |
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54 | |
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55 | union { float f; uint32_t x; } u = { f }; |
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56 | |
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57 | uint16_t bits = basetable[(u.x >> 23) & 0x1ff]; |
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58 | bits |= (u.x & 0x007fffff) >> shifttable[(u.x >> 23) & 0x1ff]; |
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59 | return makebits(bits); |
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60 | } |
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61 | |
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62 | /* This method is faster than the OpenEXR implementation (very often |
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63 | * used, eg. in Ogre), with the additional benefit of rounding, inspired |
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64 | * by James Tursa’s half-precision code. */ |
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65 | half half::makeslow(float f) |
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66 | { |
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67 | union { float f; uint32_t x; } u = { f }; |
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68 | |
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69 | uint16_t bits = (u.x >> 16) & 0x8000; /* Get the sign */ |
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70 | uint16_t m = (u.x >> 12) & 0x07ff; /* Keep one extra bit for rounding */ |
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71 | unsigned int e = (u.x >> 23) & 0xff; /* Using int is faster here */ |
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72 | |
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73 | /* If zero, or denormal, or exponent underflows too much for a denormal, |
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74 | * return signed zero. */ |
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75 | if (e < 103) |
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76 | return makebits(bits); |
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77 | |
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78 | /* If NaN, return NaN. If Inf or exponent overflow, return Inf. */ |
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79 | if (e > 142) |
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80 | { |
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81 | bits |= 0x7c00u; |
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82 | /* If exponent was 0xff and one mantissa bit was set, it means NaN, |
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83 | * not Inf, so make sure we set one mantissa bit too. */ |
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84 | bits |= e == 255 && (u.x & 0x007fffffu); |
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85 | return makebits(bits); |
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86 | } |
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87 | |
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88 | /* If exponent underflows but not too much, return a denormal */ |
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89 | if (e < 113) |
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90 | { |
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91 | m |= 0x0800u; |
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92 | /* Extra rounding may overflow and set mantissa to 0 and exponent |
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93 | * to 1, which is OK. */ |
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94 | bits |= (m >> (114 - e)) + ((m >> (113 - e)) & 1); |
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95 | return makebits(bits); |
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96 | } |
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97 | |
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98 | bits |= ((e - 112) << 10) | (m >> 1); |
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99 | /* Extra rounding. An overflow will set mantissa to 0 and increment |
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100 | * the exponent, which is OK. */ |
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101 | bits += m & 1; |
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102 | return makebits(bits); |
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103 | } |
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104 | |
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105 | half::operator float() const |
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106 | { |
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107 | union { float f; uint32_t x; } u; |
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108 | |
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109 | uint32_t s = (m_bits & 0x8000u) << 16; |
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110 | |
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111 | if ((m_bits & 0x7fffu) == 0) |
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112 | { |
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113 | u.x = (uint32_t)m_bits << 16; |
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114 | return u.f; |
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115 | } |
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116 | |
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117 | uint32_t e = m_bits & 0x7c00u; |
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118 | uint32_t m = m_bits & 0x03ffu; |
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119 | |
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120 | if (e == 0) |
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121 | { |
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122 | static int const shifttable[32] = |
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123 | { |
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124 | 10, 1, 9, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 7, 0, |
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125 | 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 5, 6, 0, |
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126 | }; |
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127 | |
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128 | uint32_t v = m | (m >> 1); |
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129 | v |= v >> 2; |
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130 | v |= v >> 4; |
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131 | v |= v >> 8; |
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132 | |
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133 | e = shifttable[(v * 0x07C4ACDDU) >> 27]; |
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134 | m <<= e; |
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135 | |
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136 | /* We don't have to remove the 10th mantissa bit because it gets |
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137 | * added to our underestimated exponent. */ |
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138 | u.x = s | (((112 - e) << 23) + (m << 13)); |
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139 | return u.f; |
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140 | } |
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141 | |
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142 | if (e == 0x7c00u) |
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143 | { |
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144 | /* The amd64 pipeline likes the if() better than a ternary operator |
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145 | * or any other trick I could find. --sam */ |
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146 | if (m == 0) |
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147 | u.x = s | 0x7f800000u; |
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148 | else |
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149 | u.x = s | 0x7fc00000u; |
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150 | |
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151 | return u.f; |
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152 | } |
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153 | |
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154 | u.x = s | (((e >> 10) + 112) << 23) | (m << 13); |
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155 | |
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156 | return u.f; |
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157 | } |
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158 | |
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159 | } /* namespace lol */ |
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160 | |
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