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<a href="a00125.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> // ratio -*- C++ -*-</div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> </div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> // Copyright (C) 2008-2018 Free Software Foundation, Inc.</div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> //</div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> // This file is part of the GNU ISO C++ Library. This library is free</div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> // software; you can redistribute it and/or modify it under the</div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> // terms of the GNU General Public License as published by the</div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> // Free Software Foundation; either version 3, or (at your option)</div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> // any later version.</div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> // This library is distributed in the hope that it will be useful,</div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> // but WITHOUT ANY WARRANTY; without even the implied warranty of</div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> // GNU General Public License for more details.</div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> // Under Section 7 of GPL version 3, you are granted additional</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> // permissions described in the GCC Runtime Library Exception, version</div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> // 3.1, as published by the Free Software Foundation.</div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> // You should have received a copy of the GNU General Public License and</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> // a copy of the GCC Runtime Library Exception along with this program;</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> // <http://www.gnu.org/licenses/>.</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> /** @file include/ratio</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  * This is a Standard C++ Library header.</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  */</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> #ifndef _GLIBCXX_RATIO</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> #define _GLIBCXX_RATIO 1</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> #pragma GCC system_header</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> #if __cplusplus < 201103L</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> # include <bits/c++0x_warning.h></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> #else</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> #include <type_traits></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> #include <cstdint></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> </div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> #ifdef _GLIBCXX_USE_C99_STDINT_TR1</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> </div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> namespace std _GLIBCXX_VISIBILITY(default)</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> {</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> _GLIBCXX_BEGIN_NAMESPACE_VERSION</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  /**</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  * @defgroup ratio Rational Arithmetic</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  * @ingroup utilities</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  *</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  * Compile time representation of finite rational numbers.</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  * @{</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  */</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  template<intmax_t _Pn></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  struct __static_sign</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  { };</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  template<intmax_t _Pn></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  struct __static_abs</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  { };</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  template<intmax_t _Pn, intmax_t _Qn></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  struct __static_gcd</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  : __static_gcd<_Qn, (_Pn % _Qn)></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  { };</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  template<intmax_t _Pn></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  struct __static_gcd<_Pn, 0></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  : integral_constant<intmax_t, __static_abs<_Pn>::value></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  { };</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> </div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  template<intmax_t _Qn></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  struct __static_gcd<0, _Qn></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  : integral_constant<intmax_t, __static_abs<_Qn>::value></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  { };</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  // Let c = 2^(half # of bits in an intmax_t)</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  // The multiplication of N and M becomes,</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  // Multiplication is safe if each term and the sum of the terms</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  // is representable by intmax_t.</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  template<intmax_t _Pn, intmax_t _Qn></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  struct __safe_multiply</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  {</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  private:</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  static_assert(__a1 == 0 || __b1 == 0,</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  "overflow in multiplication");</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  "overflow in multiplication");</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  static_assert(__b0 * __a0 <= __INTMAX_MAX__,</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  "overflow in multiplication");</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  static_assert((__a0 * __b1 + __b0 * __a1) * __c</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <= __INTMAX_MAX__ - __b0 * __a0,</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  "overflow in multiplication");</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> </div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  public:</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  static const intmax_t value = _Pn * _Qn;</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  };</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> </div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  // Some double-precision utilities, where numbers are represented as</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  // __hi*2^(8*sizeof(uintmax_t)) + __lo.</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  struct __big_less</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  : integral_constant<bool, (__hi1 < __hi2</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  || (__hi1 == __hi2 && __lo1 < __lo2))></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  { };</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> </div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  struct __big_add</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  {</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  static constexpr uintmax_t __lo = __lo1 + __lo2;</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  static constexpr uintmax_t __hi = (__hi1 + __hi2 +</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  (__lo1 + __lo2 < __lo1)); // carry</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  };</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  // Subtract a number from a bigger one.</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  struct __big_sub</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  {</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value,</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  "Internal library error");</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  static constexpr uintmax_t __lo = __lo1 - __lo2;</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  static constexpr uintmax_t __hi = (__hi1 - __hi2 -</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  (__lo1 < __lo2)); // carry</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  };</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  // Same principle as __safe_multiply.</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  template<uintmax_t __x, uintmax_t __y></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  struct __big_mul</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  {</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  private:</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  static constexpr uintmax_t __x0 = __x % __c;</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  static constexpr uintmax_t __x1 = __x / __c;</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  static constexpr uintmax_t __y0 = __y % __c;</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  static constexpr uintmax_t __y1 = __y / __c;</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  static constexpr uintmax_t __x0y0 = __x0 * __y0;</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  static constexpr uintmax_t __x0y1 = __x0 * __y1;</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  static constexpr uintmax_t __x1y0 = __x1 * __y0;</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  static constexpr uintmax_t __x1y1 = __x1 * __y1;</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry...</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  static constexpr uintmax_t __mix_lo = __mix * __c;</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  static constexpr uintmax_t __mix_hi</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res;</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  public:</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  static constexpr uintmax_t __hi = _Res::__hi;</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  static constexpr uintmax_t __lo = _Res::__lo;</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  };</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> </div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  // Adapted from __udiv_qrnnd_c in longlong.h</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  // This version assumes that the high bit of __d is 1.</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d></div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  struct __big_div_impl</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  {</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  private:</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)),</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  "Internal library error");</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  static_assert(__n1 < __d, "Internal library error");</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  static constexpr uintmax_t __d1 = __d / __c;</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  static constexpr uintmax_t __d0 = __d % __c;</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> </div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  static constexpr uintmax_t __q1x = __n1 / __d1;</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  static constexpr uintmax_t __r1x = __n1 % __d1;</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  static constexpr uintmax_t __m = __q1x * __d0;</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c;</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  static constexpr uintmax_t __r1z = __r1y + __d;</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  static constexpr uintmax_t __r1</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m))</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  ? (__r1z + __d) : __r1z : __r1y) - __m;</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  static constexpr uintmax_t __q1</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  = __q1x - ((__r1y < __m)</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0);</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  static constexpr uintmax_t __q0x = __r1 / __d1;</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  static constexpr uintmax_t __r0x = __r1 % __d1;</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  static constexpr uintmax_t __n = __q0x * __d0;</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c;</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  static constexpr uintmax_t __r0z = __r0y + __d;</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  static constexpr uintmax_t __r0</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n))</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  ? (__r0z + __d) : __r0z : __r0y) - __n;</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  static constexpr uintmax_t __q0</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  = __q0x - ((__r0y < __n) ? ((__r0z >= __d)</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  && (__r0z < __n)) ? 2 : 1 : 0);</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  public:</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  static constexpr uintmax_t __quot = __q1 * __c + __q0;</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  static constexpr uintmax_t __rem = __r0;</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> </div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  private:</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  typedef __big_mul<__quot, __d> _Prod;</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum;</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0,</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  "Internal library error");</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  };</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> </div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  struct __big_div</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  {</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  private:</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  static_assert(__d != 0, "Internal library error");</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  static_assert(sizeof (uintmax_t) == sizeof (unsigned long long),</div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  "This library calls __builtin_clzll on uintmax_t, which "</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  "is unsafe on your platform. Please complain to "</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  "http://gcc.gnu.org/bugzilla/");</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  static constexpr int __shift = __builtin_clzll(__d);</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift;</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0;</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  static constexpr uintmax_t __c1 = uintmax_t(1) << __shift;</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift;</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  static constexpr uintmax_t __new_d = __d * __c1;</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  static constexpr uintmax_t __new_n0 = __n0 * __c1;</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1;</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0;</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top;</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res;</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  public:</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  static constexpr uintmax_t __quot_hi = __n1 / __d;</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  static constexpr uintmax_t __quot_lo = _Res::__quot;</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  static constexpr uintmax_t __rem = _Res::__rem / __c1;</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> </div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  private:</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  typedef __big_mul<__quot_lo, __d> _P0;</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  typedef __big_mul<__quot_hi, __d> _P1;</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum;</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  // No overflow.</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  static_assert(_P1::__hi == 0, "Internal library error");</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  static_assert(_Sum::__hi >= _P0::__hi, "Internal library error");</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  // Matches the input data.</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0,</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  "Internal library error");</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  static_assert(__rem < __d, "Internal library error");</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  };</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span> </div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  /**</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  * @brief Provides compile-time rational arithmetic.</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  *</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  * This class template represents any finite rational number with a</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  * numerator and denominator representable by compile-time constants of</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  * type intmax_t. The ratio is simplified when instantiated.</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  *</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  * For example:</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  * @code</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  * std::ratio<7,-21>::num == -1;</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  * std::ratio<7,-21>::den == 3;</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  * @endcode</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  *</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  */</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  template<intmax_t _Num, intmax_t _Den = 1></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  struct ratio</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  {</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  static_assert(_Den != 0, "denominator cannot be zero");</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  "out of range");</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  // Note: sign(N) * abs(N) == N</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  static constexpr intmax_t num =</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span> </div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  static constexpr intmax_t den =</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span> </div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  typedef ratio<num, den> type;</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  };</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> </div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  template<intmax_t _Num, intmax_t _Den></div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  constexpr intmax_t ratio<_Num, _Den>::num;</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> </div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  template<intmax_t _Num, intmax_t _Den></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  constexpr intmax_t ratio<_Num, _Den>::den;</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span> </div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  struct __ratio_multiply</div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  {</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  private:</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  static const intmax_t __gcd1 =</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  __static_gcd<_R1::num, _R2::den>::value;</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  static const intmax_t __gcd2 =</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  __static_gcd<_R2::num, _R1::den>::value;</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span> </div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  public:</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  typedef ratio<</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  __safe_multiply<(_R1::num / __gcd1),</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  (_R2::num / __gcd2)>::value,</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  __safe_multiply<(_R1::den / __gcd2),</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  (_R2::den / __gcd1)>::value> type;</div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> </div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  static constexpr intmax_t num = type::num;</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  static constexpr intmax_t den = type::den;</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  };</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span> </div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  constexpr intmax_t __ratio_multiply<_R1, _R2>::num;</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  constexpr intmax_t __ratio_multiply<_R1, _R2>::den;</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> </div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  /// ratio_multiply</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type;</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span> </div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  struct __ratio_divide</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  {</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  static_assert(_R2::num != 0, "division by 0");</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  typedef typename __ratio_multiply<</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  _R1,</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  ratio<_R2::den, _R2::num>>::type type;</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span> </div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  static constexpr intmax_t num = type::num;</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  static constexpr intmax_t den = type::den;</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  };</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  constexpr intmax_t __ratio_divide<_R1, _R2>::num;</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  constexpr intmax_t __ratio_divide<_R1, _R2>::den;</div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span> </div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  /// ratio_divide</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  using ratio_divide = typename __ratio_divide<_R1, _R2>::type;</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span> </div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  /// ratio_equal</div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  struct ratio_equal</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den></div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  { };</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span> </div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  /// ratio_not_equal</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  struct ratio_not_equal</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  : integral_constant<bool, !ratio_equal<_R1, _R2>::value></div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  { };</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span> </div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  // Both numbers are positive.</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  template<typename _R1, typename _R2,</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  typename _Left = __big_mul<_R1::num,_R2::den>,</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  typename _Right = __big_mul<_R2::num,_R1::den> ></div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  struct __ratio_less_impl_1</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo,</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  _Right::__hi, _Right::__lo>::value></div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  { };</div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span> </div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  template<typename _R1, typename _R2,</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  bool = (_R1::num == 0 || _R2::num == 0</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  || (__static_sign<_R1::num>::value</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  != __static_sign<_R2::num>::value)),</div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  bool = (__static_sign<_R1::num>::value == -1</div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  && __static_sign<_R2::num>::value == -1)></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  struct __ratio_less_impl</div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  : __ratio_less_impl_1<_R1, _R2>::type</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  { };</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span> </div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  struct __ratio_less_impl<_R1, _R2, true, false></div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  : integral_constant<bool, _R1::num < _R2::num></div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  { };</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  struct __ratio_less_impl<_R1, _R2, false, true></div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>,</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  ratio<-_R1::num, _R1::den> >::type</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  { };</div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span> </div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  /// ratio_less</div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  struct ratio_less</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  : __ratio_less_impl<_R1, _R2>::type</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  { };</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span> </div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  /// ratio_less_equal</div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  struct ratio_less_equal</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  : integral_constant<bool, !ratio_less<_R2, _R1>::value></div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  { };</div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span> </div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  /// ratio_greater</div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  struct ratio_greater</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  : integral_constant<bool, ratio_less<_R2, _R1>::value></div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  { };</div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span> </div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  /// ratio_greater_equal</div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  struct ratio_greater_equal</div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  : integral_constant<bool, !ratio_less<_R1, _R2>::value></div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  { };</div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span> </div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span> #if __cplusplus > 201402L</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  template <typename _R1, typename _R2></div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value;</div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  template <typename _R1, typename _R2></div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value;</div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  template <typename _R1, typename _R2></div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value;</div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  template <typename _R1, typename _R2></div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  inline constexpr bool ratio_less_equal_v =</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  ratio_less_equal<_R1, _R2>::value;</div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  template <typename _R1, typename _R2></div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value;</div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  template <typename _R1, typename _R2></div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  inline constexpr bool ratio_greater_equal_v</div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  = ratio_greater_equal<_R1, _R2>::value;</div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span> #endif // C++17</div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> </div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  template<typename _R1, typename _R2,</div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  bool = (_R1::num >= 0),</div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  bool = (_R2::num >= 0),</div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>,</div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  ratio<__static_abs<_R2::num>::value, _R2::den> >::value></div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  struct __ratio_add_impl</div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  {</div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  private:</div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  typedef typename __ratio_add_impl<</div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  ratio<-_R1::num, _R1::den>,</div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  ratio<-_R2::num, _R2::den> >::type __t;</div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  public:</div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  typedef ratio<-__t::num, __t::den> type;</div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  };</div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span> </div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  // True addition of nonnegative numbers.</div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  template<typename _R1, typename _R2, bool __b></div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  struct __ratio_add_impl<_R1, _R2, true, true, __b></div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  {</div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  private:</div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value;</div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  static constexpr uintmax_t __d2 = _R2::den / __g;</div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  typedef __big_mul<_R1::den, __d2> __d;</div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  typedef __big_mul<_R1::num, _R2::den / __g> __x;</div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  typedef __big_mul<_R2::num, _R1::den / __g> __y;</div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n;</div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  static_assert(__n::__hi >= __x::__hi, "Internal library error");</div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  typedef __big_div<__n::__hi, __n::__lo, __g> __ng;</div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value;</div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final;</div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  static_assert(__n_final::__rem == 0, "Internal library error");</div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  static_assert(__n_final::__quot_hi == 0 &&</div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition");</div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  typedef __big_mul<_R1::den / __g2, __d2> __d_final;</div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  static_assert(__d_final::__hi == 0 &&</div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  __d_final::__lo <= __INTMAX_MAX__, "overflow in addition");</div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  public:</div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  typedef ratio<__n_final::__quot_lo, __d_final::__lo> type;</div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  };</div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span> </div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  struct __ratio_add_impl<_R1, _R2, false, true, true></div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  : __ratio_add_impl<_R2, _R1></div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  { };</div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span> </div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  // True subtraction of nonnegative numbers yielding a nonnegative result.</div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  struct __ratio_add_impl<_R1, _R2, true, false, false></div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  {</div><div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  private:</div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value;</div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  static constexpr uintmax_t __d2 = _R2::den / __g;</div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  typedef __big_mul<_R1::den, __d2> __d;</div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  typedef __big_mul<_R1::num, _R2::den / __g> __x;</div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  typedef __big_mul<-_R2::num, _R1::den / __g> __y;</div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n;</div><div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  typedef __big_div<__n::__hi, __n::__lo, __g> __ng;</div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value;</div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final;</div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  static_assert(__n_final::__rem == 0, "Internal library error");</div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  static_assert(__n_final::__quot_hi == 0 &&</div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition");</div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  typedef __big_mul<_R1::den / __g2, __d2> __d_final;</div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  static_assert(__d_final::__hi == 0 &&</div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  __d_final::__lo <= __INTMAX_MAX__, "overflow in addition");</div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  public:</div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  typedef ratio<__n_final::__quot_lo, __d_final::__lo> type;</div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  };</div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span> </div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  struct __ratio_add</div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  {</div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  typedef typename __ratio_add_impl<_R1, _R2>::type type;</div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  static constexpr intmax_t num = type::num;</div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  static constexpr intmax_t den = type::den;</div><div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  };</div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span> </div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  constexpr intmax_t __ratio_add<_R1, _R2>::num;</div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span> </div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  constexpr intmax_t __ratio_add<_R1, _R2>::den;</div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span> </div><div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  /// ratio_add</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  using ratio_add = typename __ratio_add<_R1, _R2>::type;</div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span> </div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  struct __ratio_subtract</div><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  {</div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  typedef typename __ratio_add<</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  _R1,</div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  ratio<-_R2::num, _R2::den>>::type type;</div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span> </div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  static constexpr intmax_t num = type::num;</div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  static constexpr intmax_t den = type::den;</div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  };</div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span> </div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  constexpr intmax_t __ratio_subtract<_R1, _R2>::num;</div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span> </div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  constexpr intmax_t __ratio_subtract<_R1, _R2>::den;</div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span> </div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  /// ratio_subtract</div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  template<typename _R1, typename _R2></div><div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type;</div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span> </div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span> </div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  typedef ratio<1, 1000000000000000000> atto;</div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  typedef ratio<1, 1000000000000000> femto;</div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  typedef ratio<1, 1000000000000> pico;</div><div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  typedef ratio<1, 1000000000> nano;</div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  typedef ratio<1, 1000000> micro;</div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  typedef ratio<1, 1000> milli;</div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  typedef ratio<1, 100> centi;</div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  typedef ratio<1, 10> deci;</div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  typedef ratio< 10, 1> deca;</div><div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  typedef ratio< 100, 1> hecto;</div><div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  typedef ratio< 1000, 1> kilo;</div><div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  typedef ratio< 1000000, 1> mega;</div><div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  typedef ratio< 1000000000, 1> giga;</div><div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  typedef ratio< 1000000000000, 1> tera;</div><div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  typedef ratio< 1000000000000000, 1> peta;</div><div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  typedef ratio< 1000000000000000000, 1> exa;</div><div class="line"><a name="l00546"></a><span class="lineno"> 546</span> </div><div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  // @} group ratio</div><div class="line"><a name="l00548"></a><span class="lineno"> 548</span> _GLIBCXX_END_NAMESPACE_VERSION</div><div class="line"><a name="l00549"></a><span class="lineno"> 549</span> } // namespace</div><div class="line"><a name="l00550"></a><span class="lineno"> 550</span> </div><div class="line"><a name="l00551"></a><span class="lineno"> 551</span> #endif //_GLIBCXX_USE_C99_STDINT_TR1</div><div class="line"><a name="l00552"></a><span class="lineno"> 552</span> </div><div class="line"><a name="l00553"></a><span class="lineno"> 553</span> #endif // C++11</div><div class="line"><a name="l00554"></a><span class="lineno"> 554</span> </div><div class="line"><a name="l00555"></a><span class="lineno"> 555</span> #endif //_GLIBCXX_RATIO</div></div><!-- fragment --></div><!-- contents -->
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