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 <cstring> |
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16 | #include <cstdio> |
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17 | |
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18 | #include "core.h" |
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19 | |
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20 | using namespace std; |
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21 | |
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22 | namespace lol |
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23 | { |
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24 | |
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25 | real::real(float f) |
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26 | { |
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27 | union { float f; uint32_t x; } u = { f }; |
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28 | |
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29 | uint32_t sign = u.x & 0x80000000u; |
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30 | uint32_t exponent = (u.x >> 23) & 0xff; |
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31 | |
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32 | switch (exponent) |
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33 | { |
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34 | case 0x00: |
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35 | case 0xff: |
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36 | m_signexp = sign | exponent; |
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37 | break; |
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38 | default: |
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39 | m_signexp = sign | (exponent + (1 << 30) - (1 << 7)); |
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40 | break; |
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41 | } |
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42 | |
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43 | m_mantissa[0] = u.x >> 7; |
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44 | m_mantissa[1] = u.x << 9; |
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45 | memset(m_mantissa + 2, 0, sizeof(m_mantissa) - sizeof(m_mantissa[0])); |
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46 | } |
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47 | |
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48 | real::operator float() const |
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49 | { |
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50 | union { float f; uint32_t x; } u; |
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51 | |
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52 | uint32_t sign = m_signexp & 0x80000000u; |
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53 | uint32_t exponent = m_signexp & 0x7fffffffu; |
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54 | uint32_t mantissa = (m_mantissa[0] << 7) | (m_mantissa[1] >> 9); |
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55 | |
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56 | int e = (int)exponent - (1 << 30) + (1 << 7); |
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57 | |
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58 | if (e < 0) |
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59 | u.x = sign; |
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60 | else if (e >= 0xff) |
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61 | u.x = sign | (0xff << 23); |
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62 | else |
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63 | u.x = sign | (e << 23) | mantissa; |
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64 | |
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65 | return u.f; |
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66 | } |
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67 | |
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68 | real real::operator -() const |
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69 | { |
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70 | real ret = *this; |
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71 | ret.m_signexp ^= 0x80000000u; |
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72 | return ret; |
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73 | } |
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74 | |
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75 | real real::operator +(real const &x) const |
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76 | { |
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77 | if (x.m_signexp << 1 == 0) |
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78 | return *this; |
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79 | |
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80 | /* Ensure both arguments are positive. Otherwise, switch signs, |
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81 | * or replace + with -). */ |
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82 | if (m_signexp >> 31) |
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83 | return -(-*this + -x); |
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84 | |
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85 | if (x.m_signexp >> 31) |
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86 | return *this - x; |
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87 | |
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88 | /* Ensure *this is the larger exponent (no need to be strictly larger, |
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89 | * as in subtraction). Otherwise, switch. */ |
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90 | if ((m_signexp << 1) < (x.m_signexp << 1)) |
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91 | return x + *this; |
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92 | |
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93 | real ret; |
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94 | |
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95 | int e1 = m_signexp - (1 << 30) + 1; |
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96 | int e2 = x.m_signexp - (1 << 30) + 1; |
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97 | |
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98 | int bigoff = (e1 - e2) / (sizeof(uint16_t) * 8); |
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99 | int off = e1 - e2 - bigoff * (sizeof(uint16_t) * 8); |
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100 | |
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101 | ret.m_signexp = m_signexp; |
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102 | |
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103 | uint32_t carry = 0; |
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104 | for (int i = BIGITS; i--; ) |
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105 | { |
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106 | carry += m_mantissa[i]; |
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107 | if (i - bigoff >= 0) |
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108 | carry += x.m_mantissa[i - bigoff] >> off; |
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109 | else if (i - bigoff == -1) |
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110 | carry += 0x0001u >> off; |
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111 | |
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112 | if (i - bigoff > 0) |
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113 | carry += (x.m_mantissa[i - bigoff - 1] << (16 - off)) & 0xffffu; |
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114 | else if (i - bigoff == 0) |
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115 | carry += 0x0001u << (16 - off); |
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116 | |
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117 | ret.m_mantissa[i] = carry; |
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118 | carry >>= 16; |
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119 | } |
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120 | |
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121 | /* Renormalise in case we overflowed the mantissa */ |
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122 | if (carry) |
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123 | { |
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124 | carry--; |
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125 | for (int i = 0; i < BIGITS; i++) |
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126 | { |
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127 | uint16_t tmp = ret.m_mantissa[i]; |
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128 | ret.m_mantissa[i] = (carry << 15) | (tmp >> 1); |
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129 | carry = tmp & 0x0001u; |
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130 | } |
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131 | ret.m_signexp++; |
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132 | } |
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133 | |
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134 | return ret; |
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135 | } |
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136 | |
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137 | real real::operator -(real const &x) const |
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138 | { |
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139 | if (x.m_signexp << 1 == 0) |
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140 | return *this; |
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141 | |
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142 | /* Ensure both arguments are positive. Otherwise, switch signs, |
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143 | * or replace - with +). */ |
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144 | if (m_signexp >> 31) |
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145 | return -(-*this + x); |
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146 | |
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147 | if (x.m_signexp >> 31) |
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148 | return (*this) + (-x); |
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149 | |
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150 | /* Ensure *this is larger than x */ |
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151 | if (*this < x) |
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152 | return -(x - *this); |
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153 | |
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154 | real ret; |
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155 | |
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156 | int e1 = m_signexp - (1 << 30) + 1; |
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157 | int e2 = x.m_signexp - (1 << 30) + 1; |
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158 | |
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159 | int bigoff = (e1 - e2) / (sizeof(uint16_t) * 8); |
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160 | int off = e1 - e2 - bigoff * (sizeof(uint16_t) * 8); |
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161 | |
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162 | ret.m_signexp = m_signexp; |
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163 | |
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164 | int32_t carry = 0; |
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165 | for (int i = 0; i < bigoff; i++) |
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166 | { |
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167 | carry -= x.m_mantissa[BIGITS - i]; |
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168 | carry = (carry & 0xffff0000u) | (carry >> 16); |
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169 | } |
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170 | carry -= x.m_mantissa[BIGITS - 1 - bigoff] & ((1 << off) - 1); |
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171 | carry /= (1 << off); |
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172 | |
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173 | for (int i = BIGITS; i--; ) |
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174 | { |
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175 | carry += m_mantissa[i]; |
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176 | if (i - bigoff >= 0) |
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177 | carry -= x.m_mantissa[i - bigoff] >> off; |
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178 | else if (i - bigoff == -1) |
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179 | carry -= 0x0001u >> off; |
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180 | |
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181 | if (i - bigoff > 0) |
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182 | carry -= (x.m_mantissa[i - bigoff - 1] << (16 - off)) & 0xffffu; |
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183 | else if (i - bigoff == 0) |
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184 | carry -= 0x0001u << (16 - off); |
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185 | |
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186 | ret.m_mantissa[i] = carry; |
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187 | carry = (carry & 0xffff0000u) | (carry >> 16); |
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188 | } |
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189 | |
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190 | carry += 1; |
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191 | |
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192 | /* Renormalise if we underflowed the mantissa */ |
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193 | if (carry == 0) |
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194 | { |
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195 | /* How much do we need to shift the mantissa? FIXME: this could |
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196 | * be computed above */ |
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197 | off = 0; |
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198 | for (int i = 0; i < BIGITS; i++) |
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199 | { |
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200 | if (!ret.m_mantissa[i]) |
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201 | { |
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202 | off += sizeof(uint16_t) * 8; |
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203 | continue; |
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204 | } |
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205 | |
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206 | for (uint16_t tmp = ret.m_mantissa[i]; tmp < 0x8000u; tmp <<= 1) |
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207 | off++; |
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208 | break; |
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209 | } |
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210 | if (off == BIGITS * sizeof(uint16_t) * 8) |
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211 | ret.m_signexp &= 0x80000000u; |
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212 | else |
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213 | { |
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214 | off++; /* Shift one more to get rid of the leading one */ |
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215 | ret.m_signexp -= off; |
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216 | |
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217 | bigoff = off / (sizeof(uint16_t) * 8); |
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218 | off -= bigoff * sizeof(uint16_t) * 8; |
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219 | |
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220 | for (int i = 0; i < BIGITS; i++) |
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221 | { |
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222 | uint16_t tmp = 0; |
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223 | if (i + bigoff < BIGITS) |
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224 | tmp |= ret.m_mantissa[i + bigoff] << off; |
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225 | if (i + bigoff + 1 < BIGITS) |
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226 | tmp |= ret.m_mantissa[i + bigoff + 1] >> (16 - off); |
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227 | ret.m_mantissa[i] = tmp; |
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228 | } |
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229 | } |
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230 | } |
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231 | |
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232 | return ret; |
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233 | } |
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234 | |
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235 | real real::operator *(real const &x) const |
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236 | { |
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237 | real ret; |
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238 | |
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239 | ret.m_signexp = (m_signexp ^ x.m_signexp) & 0x80000000u; |
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240 | int e = (m_signexp & 0x7fffffffu) - (1 << 30) + 1 |
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241 | + (x.m_signexp & 0x7fffffffu) - (1 << 30) + 1; |
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242 | |
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243 | /* Accumulate low order product; no need to store it, we just |
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244 | * want the carry value */ |
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245 | uint32_t carry = 0; |
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246 | for (int i = 0; i < BIGITS; i++) |
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247 | { |
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248 | for (int j = 0; j < i + 1; j++) |
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249 | carry += m_mantissa[BIGITS - 1 - j] |
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250 | * x.m_mantissa[BIGITS - 1 + j - i]; |
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251 | carry >>= 16; |
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252 | } |
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253 | |
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254 | for (int i = 0; i < BIGITS; i++) |
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255 | { |
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256 | for (int j = i + 1; j < BIGITS; j++) |
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257 | carry += m_mantissa[BIGITS - 1 - j] |
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258 | * x.m_mantissa[j - 1 - i]; |
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259 | |
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260 | carry += m_mantissa[BIGITS - 1 - i]; |
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261 | carry += x.m_mantissa[BIGITS - 1 - i]; |
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262 | ret.m_mantissa[BIGITS - 1 - i] = carry & 0xffffu; |
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263 | carry >>= 16; |
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264 | } |
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265 | |
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266 | /* Renormalise in case we overflowed the mantissa */ |
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267 | if (carry) |
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268 | { |
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269 | carry--; |
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270 | for (int i = 0; i < BIGITS; i++) |
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271 | { |
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272 | uint16_t tmp = ret.m_mantissa[i]; |
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273 | ret.m_mantissa[i] = (carry << 15) | (tmp >> 1); |
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274 | carry = tmp & 0x0001u; |
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275 | } |
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276 | e++; |
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277 | } |
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278 | |
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279 | ret.m_signexp |= e + (1 << 30) - 1; |
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280 | |
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281 | return ret; |
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282 | } |
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283 | |
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284 | bool real::operator <(real const &x) const |
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285 | { |
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286 | /* Ensure both numbers are positive */ |
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287 | if (m_signexp >> 31) |
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288 | return (x.m_signexp >> 31) ? -*this > -x : true; |
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289 | |
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290 | if (x.m_signexp >> 31) |
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291 | return false; |
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292 | |
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293 | /* Compare all relevant bits */ |
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294 | if (m_signexp != x.m_signexp) |
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295 | return m_signexp < x.m_signexp; |
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296 | |
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297 | for (int i = 0; i < BIGITS; i++) |
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298 | if (m_mantissa[i] != x.m_mantissa[i]) |
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299 | return m_mantissa[i] < x.m_mantissa[i]; |
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300 | |
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301 | return false; |
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302 | } |
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303 | |
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304 | bool real::operator <=(real const &x) const |
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305 | { |
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306 | return !(*this > x); |
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307 | } |
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308 | |
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309 | bool real::operator >(real const &x) const |
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310 | { |
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311 | /* Ensure both numbers are positive */ |
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312 | if (m_signexp >> 31) |
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313 | return (x.m_signexp >> 31) ? -*this < -x : false; |
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314 | |
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315 | if (x.m_signexp >> 31) |
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316 | return true; |
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317 | |
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318 | /* Compare all relevant bits */ |
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319 | if (m_signexp != x.m_signexp) |
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320 | return m_signexp > x.m_signexp; |
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321 | |
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322 | for (int i = 0; i < BIGITS; i++) |
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323 | if (m_mantissa[i] != x.m_mantissa[i]) |
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324 | return m_mantissa[i] > x.m_mantissa[i]; |
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325 | |
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326 | return false; |
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327 | } |
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328 | |
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329 | bool real::operator >=(real const &x) const |
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330 | { |
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331 | return !(*this < x); |
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332 | } |
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333 | |
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334 | void real::print() const |
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335 | { |
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336 | printf("%x %08x ", m_signexp >> 31, (m_signexp << 1) >> 1); |
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337 | for (int i = 0; i < BIGITS; i++) |
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338 | printf("%04x ", m_mantissa[i]); |
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339 | printf("\n"); |
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340 | } |
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341 | |
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342 | } /* namespace lol */ |
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343 | |
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