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 | /* These macros implement a finite iterator useful to build lookup |
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23 | * tables. For instance, S64(0) will call S1(x) for all values of x |
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24 | * between 0 and 63. |
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25 | * Due to the exponential behaviour of the calls, the stress on the |
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26 | * compiler may be important. */ |
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27 | #define S4(x) S1((x)), S1((x)+1), S1((x)+2), S1((x)+3) |
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28 | #define S16(x) S4((x)), S4((x)+4), S4((x)+8), S4((x)+12) |
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29 | #define S64(x) S16((x)), S16((x)+16), S16((x)+32), S16((x)+48) |
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30 | #define S256(x) S64((x)), S64((x)+64), S64((x)+128), S64((x)+192) |
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31 | #define S1024(x) S256((x)), S256((x)+256), S256((x)+512), S256((x)+768) |
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32 | |
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33 | /* Lookup table-based algorithm from “Fast Half Float Conversions” |
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34 | * by Jeroen van der Zijp, November 2008. No rounding is performed, |
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35 | * and some NaN values may be incorrectly converted to Inf. */ |
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36 | static inline uint16_t float_to_half_nobranch(uint32_t x) |
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37 | { |
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38 | static uint16_t const basetable[512] = |
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39 | { |
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40 | #define S1(i) (((i) < 103) ? 0x0000: \ |
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41 | ((i) < 113) ? 0x0400 >> (113 - (i)) : \ |
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42 | ((i) < 143) ? ((i) - 112) << 10 : 0x7c00) |
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43 | S256(0), |
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44 | #undef S1 |
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45 | #define S1(i) (0x8000 | (((i) < 103) ? 0x0000 : \ |
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46 | ((i) < 113) ? 0x0400 >> (113 - (i)): \ |
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47 | ((i) < 143) ? ((i) - 112) << 10 : 0x7c00)) |
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48 | S256(0), |
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49 | #undef S1 |
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50 | }; |
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51 | |
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52 | static uint8_t const shifttable[512] = |
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53 | { |
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54 | #define S1(i) (((i) < 103) ? 24 : \ |
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55 | ((i) < 113) ? 126 - (i) : \ |
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56 | ((i) < 143 || (i) == 255) ? 13 : 24) |
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57 | S256(0), S256(0), |
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58 | #undef S1 |
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59 | }; |
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60 | |
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61 | uint16_t bits = basetable[(x >> 23) & 0x1ff]; |
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62 | bits |= (x & 0x007fffff) >> shifttable[(x >> 23) & 0x1ff]; |
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63 | return bits; |
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64 | } |
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65 | |
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66 | /* This method is faster than the OpenEXR implementation (very often |
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67 | * used, eg. in Ogre), with the additional benefit of rounding, inspired |
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68 | * by James Tursa’s half-precision code. */ |
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69 | static inline uint16_t float_to_half_branch(uint32_t x) |
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70 | { |
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71 | uint16_t bits = (x >> 16) & 0x8000; /* Get the sign */ |
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72 | uint16_t m = (x >> 12) & 0x07ff; /* Keep one extra bit for rounding */ |
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73 | unsigned int e = (x >> 23) & 0xff; /* Using int is faster here */ |
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74 | |
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75 | /* If zero, or denormal, or exponent underflows too much for a denormal, |
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76 | * return signed zero. */ |
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77 | if (e < 103) |
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78 | return bits; |
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79 | |
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80 | /* If NaN, return NaN. If Inf or exponent overflow, return Inf. */ |
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81 | if (e > 142) |
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82 | { |
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83 | bits |= 0x7c00u; |
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84 | /* If exponent was 0xff and one mantissa bit was set, it means NaN, |
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85 | * not Inf, so make sure we set one mantissa bit too. */ |
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86 | bits |= e == 255 && (x & 0x007fffffu); |
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87 | return bits; |
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88 | } |
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89 | |
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90 | /* If exponent underflows but not too much, return a denormal */ |
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91 | if (e < 113) |
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92 | { |
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93 | m |= 0x0800u; |
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94 | /* Extra rounding may overflow and set mantissa to 0 and exponent |
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95 | * to 1, which is OK. */ |
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96 | bits |= (m >> (114 - e)) + ((m >> (113 - e)) & 1); |
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97 | return bits; |
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98 | } |
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99 | |
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100 | bits |= ((e - 112) << 10) | (m >> 1); |
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101 | /* Extra rounding. An overflow will set mantissa to 0 and increment |
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102 | * the exponent, which is OK. */ |
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103 | bits += m & 1; |
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104 | return bits; |
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105 | } |
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106 | |
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107 | static int const shifttable[32] = |
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108 | { |
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109 | 23, 14, 22, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 20, 0, |
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110 | 15, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 17, 0, 18, 19, 0, |
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111 | }; |
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112 | static uint32_t const shiftmagic = 0x07c4acddu; |
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113 | |
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114 | /* Lookup table-based algorithm from “Fast Half Float Conversions” |
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115 | * by Jeroen van der Zijp, November 2008. Tables are generated using |
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116 | * the C++ preprocessor, thanks to a branchless implementation also |
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117 | * used in half_to_float_branch(). This code is very fast when performing |
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118 | * conversions on arrays of values. */ |
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119 | static inline uint32_t half_to_float_nobranch(uint16_t x) |
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120 | { |
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121 | #define M3(i) ((i) | ((i) >> 1)) |
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122 | #define M7(i) (M3(i) | (M3(i) >> 2)) |
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123 | #define MF(i) (M7(i) | (M7(i) >> 4)) |
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124 | #define MFF(i) (MF(i) | (MF(i) >> 8)) |
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125 | #define E(i) shifttable[(unsigned int)(MFF(i) * shiftmagic) >> 27] |
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126 | |
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127 | static uint32_t const mantissatable[2048] = |
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128 | { |
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129 | #define S1(i) (((i) == 0) ? 0 : ((125 - E(i)) << 23) + ((i) << E(i))) |
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130 | S1024(0), |
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131 | #undef S1 |
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132 | #define S1(i) (0x38000000u + ((i) << 13)) |
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133 | S1024(0), |
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134 | #undef S1 |
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135 | }; |
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136 | |
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137 | static uint32_t const exponenttable[64] = |
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138 | { |
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139 | #define S1(i) (((i) == 0) ? 0 : \ |
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140 | ((i) < 31) ? ((i) << 23) : \ |
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141 | ((i) == 31) ? 0x47800000u : \ |
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142 | ((i) == 32) ? 0x80000000u : \ |
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143 | ((i) < 63) ? (0x80000000u + (((i) - 32) << 23)) : 0xc7800000) |
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144 | S64(0), |
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145 | #undef S1 |
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146 | }; |
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147 | |
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148 | static int const offsettable[64] = |
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149 | { |
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150 | #define S1(i) (((i) == 0 || (i) == 32) ? 0 : 1024) |
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151 | S64(0), |
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152 | #undef S1 |
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153 | }; |
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154 | |
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155 | return mantissatable[offsettable[x >> 10] + (x & 0x3ff)] |
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156 | + exponenttable[x >> 10]; |
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157 | } |
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158 | |
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159 | /* This algorithm is similar to the OpenEXR implementation, except it |
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160 | * uses branchless code in the denormal path. This is slower than the |
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161 | * table version, but will be more friendly to the cache for occasional |
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162 | * uses. */ |
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163 | static inline uint32_t half_to_float_branch(uint16_t x) |
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164 | { |
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165 | uint32_t s = (x & 0x8000u) << 16; |
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166 | |
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167 | if ((x & 0x7fffu) == 0) |
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168 | return (uint32_t)x << 16; |
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169 | |
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170 | uint32_t e = x & 0x7c00u; |
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171 | uint32_t m = x & 0x03ffu; |
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172 | |
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173 | if (e == 0) |
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174 | { |
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175 | uint32_t v = m | (m >> 1); |
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176 | v |= v >> 2; |
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177 | v |= v >> 4; |
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178 | v |= v >> 8; |
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179 | |
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180 | e = shifttable[(v * shiftmagic) >> 27]; |
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181 | |
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182 | /* We don't have to remove the 10th mantissa bit because it gets |
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183 | * added to our underestimated exponent. */ |
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184 | return s | (((125 - e) << 23) + (m << e)); |
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185 | } |
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186 | |
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187 | if (e == 0x7c00u) |
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188 | { |
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189 | /* The amd64 pipeline likes the if() better than a ternary operator |
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190 | * or any other trick I could find. --sam */ |
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191 | if (m == 0) |
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192 | return s | 0x7f800000u; |
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193 | return s | 0x7fc00000u; |
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194 | } |
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195 | |
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196 | return s | (((e >> 10) + 112) << 23) | (m << 13); |
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197 | } |
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198 | |
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199 | /* Constructor from float. Uses the non-branching version because benchmarks |
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200 | * indicate it is always twice as fast. The penalty of loading the lookup |
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201 | * tables does not seem important. */ |
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202 | half half::makefast(float f) |
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203 | { |
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204 | union { float f; uint32_t x; } u = { f }; |
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205 | return makebits(float_to_half_nobranch(u.x)); |
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206 | } |
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207 | |
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208 | /* Constructor from float with better precision. */ |
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209 | half half::makeslow(float f) |
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210 | { |
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211 | union { float f; uint32_t x; } u = { f }; |
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212 | return makebits(float_to_half_branch(u.x)); |
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213 | } |
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214 | |
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215 | /* Cast to float. Uses the branching version because loading the tables |
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216 | * for only one value is going to be cache-expensive. */ |
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217 | half::operator float() const |
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218 | { |
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219 | /* FIXME: there is a hidden "this" in this method. Export more |
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220 | * code so that it can all work in registers instead. */ |
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221 | union { float f; uint32_t x; } u; |
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222 | u.x = half_to_float_branch(bits); |
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223 | return u.f; |
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224 | } |
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225 | |
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226 | size_t half::convert(half *dst, float const *src, size_t nelem) |
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227 | { |
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228 | for (size_t i = 0; i < nelem; i++) |
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229 | { |
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230 | union { float f; uint32_t x; } u; |
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231 | u.f = *src++; |
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232 | *dst++ = makebits(float_to_half_nobranch(u.x)); |
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233 | } |
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234 | |
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235 | return nelem; |
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236 | } |
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237 | |
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238 | size_t half::convert(float *dst, half const *src, size_t nelem) |
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239 | { |
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240 | for (size_t i = 0; i < nelem; i++) |
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241 | { |
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242 | union { float f; uint32_t x; } u; |
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243 | u.x = half_to_float_nobranch((*src++).bits); |
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244 | *dst++ = u.f; |
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245 | } |
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246 | |
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247 | return nelem; |
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248 | } |
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249 | |
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250 | } /* namespace lol */ |
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251 | |
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