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<div class="title">rational.cpp</div> </div>
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<a href="rational_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*****************************************************************************/</span><span class="comment"></span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">/*!</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * \file rational.cpp</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * Author: Sergey Berezin</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * Created: Dec 12 22:00:18 GMT 2002</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * and its documentation for any purpose is hereby granted without</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * LICENSE file provided with this distribution.</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">/*****************************************************************************/</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// Class: Rational</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// Author: Sergey Berezin, 12/12/2002 (adapted from Bignum)</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">//</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// Description: Implementation of class Rational. See comments in</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// rational.h file.</span><span class="comment"></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">///////////////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"></span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#ifdef RATIONAL_GMPXX</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <gmpxx.h></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include "<a class="code" href="compat__hash__set_8h.html">compat_hash_set.h</a>"</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include "<a class="code" href="rational_8h.html">rational.h</a>"</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">namespace </span>CVC3 {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">using namespace </span>std;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="comment">// Implementation of the forward-declared internal class</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keyword">class </span>Rational::Impl : <span class="keyword">public</span> mpq_class {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="comment">// mpz_class _n;</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="comment">// Constructors</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  Impl() : mpq_class() { }</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="comment">// Constructor from integer</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="comment">// Impl(const mpz_class &x) : mpq_class(x) { }</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="comment">// Constructor from rational</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  Impl(<span class="keyword">const</span> mpq_class &x) : mpq_class(x) { }</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="comment">// Copy constructor</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  Impl(<span class="keyword">const</span> Impl &x) : mpq_class(x) { }</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// From pair of integers / strings</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  Impl(<span class="keywordtype">int</span> n, <span class="keywordtype">int</span> d) : mpq_class(n,d) { canonicalize(); }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  Impl(<span class="keyword">const</span> mpz_class& n, <span class="keyword">const</span> mpz_class& d)</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  : mpq_class(n,d) { canonicalize(); }</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">// From string(s)</span></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base): mpq_class(n, base) { canonicalize(); }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keyword">const</span> <span class="keywordtype">string</span>& d, <span class="keywordtype">int</span> base)</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  : mpq_class(n + <span class="stringliteral">"/"</span> + d, base) { canonicalize(); }</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">virtual</span> ~Impl() { }</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// Getting numerator and denominator. DON NOT ASSIGN to the result</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  mpz_class getNum() { <span class="keywordflow">return</span> get_num(); }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  mpz_class getDen() { <span class="keywordflow">return</span> get_den(); }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  };</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>  <span class="comment">// Constructors</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <a class="code" href="classCVC3_1_1Rational.html#a8f86f975b54d0a491bc909d677023467">Rational::Rational</a>() : d_n(new Impl) {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  num_created++;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  printStats();</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// Copy constructor</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  Rational::Rational(<span class="keyword">const</span> Rational &n) : d_n(new Impl(*n.d_n)) {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  num_created++;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  printStats();</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">// Private constructor</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  Rational::Rational(<span class="keyword">const</span> Impl& t): d_n(new Impl(t)) {</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  num_created++;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  printStats();</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  Rational::Rational(<span class="keywordtype">int</span> n, <span class="keywordtype">int</span> d): d_n(new Impl(n, d)) {</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  num_created++;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  printStats();</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// Constructors from strings</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">char</span>* n, <span class="keywordtype">int</span> base)</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  : d_n(new Impl(string(n), base)) {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  num_created++;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  printStats();</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">string</span>& n, <span class="keywordtype">int</span> base)</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  : d_n(new Impl(n, base)) {</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  num_created++;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  printStats();</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">char</span>* n, <span class="keyword">const</span> <span class="keywordtype">char</span>* d, <span class="keywordtype">int</span> base)</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  : d_n(new Impl(string(n), string(d), base)) {</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  num_created++;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  printStats();</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  Rational::Rational(<span class="keyword">const</span> <span class="keywordtype">string</span>& n, <span class="keyword">const</span> <span class="keywordtype">string</span>& d, <span class="keywordtype">int</span> base)</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  : d_n(new Impl(n, d, base)) {</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  num_created++;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  printStats();</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  Rational::~Rational() {</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keyword">delete</span> d_n;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_deleted = getDeleted();</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  num_deleted++;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  printStats();</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// Get components</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  Rational Rational::getNumerator()<span class="keyword"> const</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="keyword"> </span>{ <span class="keywordflow">return</span> Rational(Impl(d_n->getNum(), 1)); }</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  Rational Rational::getDenominator()<span class="keyword"> const</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="keyword"> </span>{ <span class="keywordflow">return</span> Rational(Impl(d_n->getDen(), 1)); }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordtype">bool</span> Rational::isInteger()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> 1 == d_n->getDen(); }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// Assignment</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  Rational& Rational::operator=(<span class="keyword">const</span> Rational& n) {</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">if</span>(<span class="keyword">this</span> == &n) <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">delete</span> d_n;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  d_n = <span class="keyword">new</span> Impl(*n.d_n);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  ostream &<a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(ostream &os, <span class="keyword">const</span> Rational &n) {</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">return</span>(os << n.toString());</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  }</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// Check that argument is an int and print an error message otherwise</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>  <span class="keyword">static</span> <span class="keywordtype">void</span> checkInt(<span class="keyword">const</span> Rational& n, <span class="keyword">const</span> <span class="keywordtype">string</span>& funName) {</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(n.isInteger(),</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  (<span class="stringliteral">"CVC3::Rational::"</span> + funName</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  + <span class="stringliteral">": argument is not an integer: "</span> + n.toString()).c_str());</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> </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="comment">/* Computes gcd and lcm on *integer* values. Result is always a</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment"> positive integer. In this implementation, it is guaranteed by</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment"> GMP. */</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  Rational gcd(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  mpz_class g;</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  checkInt(x, <span class="stringliteral">"gcd(*x*,y)"</span>);</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  checkInt(y, <span class="stringliteral">"gcd(x,*y*)"</span>);</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  mpz_gcd(g.get_mpz_t(), x.d_n->get_num_mpz_t(), y.d_n->get_num_mpz_t());</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  }</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  Rational gcd(<span class="keyword">const</span> vector<Rational> &v) {</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  mpz_class g(1);</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordflow">if</span>(v.size() > 0) {</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  checkInt(v[0], <span class="stringliteral">"gcd(vector<Rational>[0])"</span>);</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  g = v[0].d_n->getNum();</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=1; i<v.size(); i++) {</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  checkInt(v[i], <span class="stringliteral">"gcd(vector<Rational>)"</span>);</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">if</span>(*v[i].d_n != 0)</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  mpz_gcd(g.get_mpz_t(), g.get_mpz_t(), v[i].d_n->get_num_mpz_t());</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  Rational lcm(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  mpz_class g;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  checkInt(x, <span class="stringliteral">"lcm(*x*,y)"</span>);</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  checkInt(y, <span class="stringliteral">"lcm(x,*y*)"</span>);</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  mpz_lcm(g.get_mpz_t(), x.d_n->get_num_mpz_t(), y.d_n->get_num_mpz_t());</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(g, 1));</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  }</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>  Rational lcm(<span class="keyword">const</span> vector<Rational> &v) {</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  mpz_class g(1);</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=0; i<v.size(); i++) {</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  checkInt(v[i], <span class="stringliteral">"lcm(vector<Rational>)"</span>);</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">if</span>(*v[i].d_n != 0)</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  mpz_lcm(g.get_mpz_t(), g.get_mpz_t(), v[i].d_n->get_num_mpz_t());</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>  <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  }</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>  Rational <a class="code" href="namespaceCVC3.html#a1463331d2ef3e7d42ae05802d02271d7">abs</a>(<span class="keyword">const</span> Rational &x) {</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(<a class="code" href="namespaceCVC3.html#a1463331d2ef3e7d42ae05802d02271d7">abs</a>(*x.d_n)));</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  }</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> </div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  Rational floor(<span class="keyword">const</span> Rational &x) {</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  mpz_class q;</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  mpz_fdiv_q(q.get_mpz_t(), x.d_n->get_num_mpz_t(), x.d_n->get_den_mpz_t());</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(q,1));</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  }</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  Rational ceil(<span class="keyword">const</span> Rational &x) {</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  mpz_class q;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  mpz_cdiv_q(q.get_mpz_t(), x.d_n->get_num_mpz_t(), x.d_n->get_den_mpz_t());</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(q,1));</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  }</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> </div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  Rational mod(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  checkInt(x, <span class="stringliteral">"mod(*x*,y)"</span>);</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  checkInt(y, <span class="stringliteral">"mod(x,*y*)"</span>);</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  mpz_class r;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  mpz_mod(r.get_mpz_t(), x.d_n->get_num_mpz_t(), y.d_n->get_num_mpz_t());</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">return</span>(Rational(Rational::Impl(r,1)));</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> </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  Rational intRoot(<span class="keyword">const</span> Rational& base, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> n)</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  {</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(0,1));</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  }</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> </div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordtype">string</span> Rational::toString(<span class="keywordtype">int</span> base)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordtype">char</span> *tmp = mpq_get_str(NULL, base, d_n->get_mpq_t());</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordtype">string</span> res(tmp);</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="comment">// delete tmp;</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  free(tmp);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">return</span>(res);</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>  <span class="keywordtype">size_t</span> Rational::hash()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <a class="code" href="structHash_1_1hash_3_01const_01char_01_5_01_4.html">std::hash<const char *></a> h;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">return</span> h(toString().c_str());</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  }</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordtype">void</span> Rational::print()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  cout << (*d_n) << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">endl</a>;</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  }</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> </div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="comment">// Unary minus</span></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  Rational <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">Rational::operator-</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(- (*d_n)));</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  }</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>  Rational &Rational::operator+=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  *d_n += (*n2.d_n);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</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>  </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  Rational &Rational::operator-=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  *d_n -= (*n2.d_n);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  }</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  Rational &Rational::operator*=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  *d_n *= (*n2.d_n);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">return</span> *<span class="keyword">this</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>  </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  Rational &Rational::operator/=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  *d_n /= (*n2.d_n);</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  }</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>  <span class="keywordtype">int</span> Rational::getInt()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  checkInt(*<span class="keyword">this</span>, <span class="stringliteral">"getInt()"</span>);</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">return</span> mpz_get_si(d_n->get_num_mpz_t());</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  }</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> </div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Rational::getUnsigned()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  checkInt(*<span class="keyword">this</span>, <span class="stringliteral">"getUnsigned()"</span>);</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keywordflow">return</span> mpz_get_ui(d_n->get_num_mpz_t());</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> </div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="preprocessor"></span> <span class="keywordtype">void</span> Rational::printStats() {</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="keywordtype">int</span> &num_deleted = getDeleted();</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">if</span>(num_created % 1000 == 0 || num_deleted % 1000 == 0) {</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  std::cerr << <span class="stringliteral">"Rational("</span> << *d_n << <span class="stringliteral">"): created "</span> << num_created</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  << <span class="stringliteral">", deleted "</span> << num_deleted</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  << <span class="stringliteral">", currently alive "</span> << num_created-num_deleted</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">std::endl</a>;</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>  }</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a8e164436388f2d87c971d9bbde973c58">operator==</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">return</span>(*n1.d_n == *n2.d_n);</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> </div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#ad3e3964a0b8cd9e2749de47b053b9d97">operator<</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">return</span>(*n1.d_n < *n2.d_n);</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> </div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#abccc88aac4f7652def737f1081dc7a89">operator<=</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">return</span>(*n1.d_n <= *n2.d_n);</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  }</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>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a0d82fd3eb68860cbd01ae86b2b9e3c66">operator></a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">return</span>(*n1.d_n > *n2.d_n);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  }</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>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#af997ba8407b661bf2ffe2cb6f52c3e3b">operator>=</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordflow">return</span>(*n1.d_n >= *n2.d_n);</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>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a5aa953c549c2e103f3834c48bf6cb9a1">operator!=</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keywordflow">return</span>(*n1.d_n != *n2.d_n);</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> </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  Rational <a class="code" href="namespaceCVC3.html#a286cf8699acada708816e72c6b436b90">operator+</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n + *n2.d_n));</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  }</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  Rational <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">operator-</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordflow">return</span> Rational(Rational::Impl((*n1.d_n) - (*n2.d_n)));</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  }</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> </div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  Rational <a class="code" href="namespaceCVC3.html#a300bc9244236ebdb1bff90b0b453034c">operator*</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">return</span> Rational(Rational::Impl((*n1.d_n) * (*n2.d_n)));</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>  Rational <a class="code" href="namespaceCVC3.html#a069aa16342bb9958a3d576a18a390248">operator/</a>(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n / *n2.d_n));</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  }</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> </div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  Rational operator%(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n + *n2.d_n));</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  }</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> </div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> </div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">// Implementation of the forward-declared internal class</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keyword">class </span>Unsigned::Impl : <span class="keyword">public</span> mpz_class {</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="comment">// mpz_class _n;</span></div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="comment">// Constructors</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  Impl() : mpz_class() { }</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="comment">// Constructor from integer</span></div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="comment">// Impl(const mpz_class &x) : mpq_class(x) { }</span></div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="comment">// Constructor from rational</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  Impl(<span class="keyword">const</span> mpz_class &x) : mpz_class(x) { }</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="comment">// Copy constructor</span></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  Impl(<span class="keyword">const</span> Impl &x) : mpz_class(x) { }</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="comment">// From pair of integers / strings</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  Impl(<span class="keywordtype">int</span> n) : mpz_class(n) { }</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  Impl(<span class="keyword">const</span> mpz_class& n, <span class="keyword">const</span> mpz_class& d)</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  : mpq_class(n,d) { canonicalize(); }</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="comment">// From string(s)</span></div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base): mpz_class(n, base) { }</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keyword">virtual</span> ~Impl() { }</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> </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="comment">// Constructors</span></div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  Unsigned::Unsigned() : d_n(new Impl) { }</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="comment">// Copy constructor</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  Unsigned::Unsigned(<span class="keyword">const</span> Unsigned &n) : d_n(new Impl(*n.d_n)) { }</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>  <span class="comment">// Private constructor</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  Unsigned::Unsigned(<span class="keyword">const</span> Impl& t): d_n(new Impl(t)) { }</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="comment">// Constructors from strings</span></div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  Unsigned::Unsigned(<span class="keyword">const</span> <span class="keywordtype">char</span>* n, <span class="keywordtype">int</span> base)</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  : d_n(new Impl(string(n), base)) { }</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  Unsigned::Unsigned(<span class="keyword">const</span> <span class="keywordtype">string</span>& n, <span class="keywordtype">int</span> base)</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  : d_n(new Impl(n, base)) { }</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  Unsigned::~Unsigned() {</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="keyword">delete</span> d_n;</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>  <span class="comment">// Assignment</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  Unsigned& Unsigned::operator=(<span class="keyword">const</span> Unsigned& n) {</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">if</span>(<span class="keyword">this</span> == &n) <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <span class="keyword">delete</span> d_n;</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  d_n = <span class="keyword">new</span> Impl(*n.d_n);</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  }</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> </div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  ostream &<a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(ostream &os, <span class="keyword">const</span> Unsigned &n) {</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="keywordflow">return</span>(os << n.toString());</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> </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="comment">/* Computes gcd and lcm on *integer* values. Result is always a</span></div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment"> positive integer. In this implementation, it is guaranteed by</span></div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment"> GMP. */</span></div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span> </div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  Unsigned gcd(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  mpz_class g;</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  mpz_gcd(g, *(x.d_n), *(y.d_n));</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  }</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  </div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  Unsigned gcd(<span class="keyword">const</span> vector<Unsigned> &v) {</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  mpz_class g(1);</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="keywordflow">if</span>(v.size() > 0) {</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  g = *(v[0].d_n);</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  }</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=1; i<v.size(); i++) {</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">if</span>(*v[i].d_n != 0)</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  mpz_gcd(g, g, *(v[i].d_n));</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  }</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  }</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> </div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  Unsigned lcm(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  mpz_class g;</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  mpz_lcm(g, *x.d_n, *y.d_n);</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  }</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> </div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  Unsigned lcm(<span class="keyword">const</span> vector<Unsigned> &v) {</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  mpz_class g(1);</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> i=0; i<v.size(); i++) {</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keywordflow">if</span>(*v[i].d_n != 0)</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  mpz_lcm(g, g, *v[i].d_n);</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  }</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  }</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> </div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  Unsigned <a class="code" href="namespaceCVC3.html#a1463331d2ef3e7d42ae05802d02271d7">abs</a>(<span class="keyword">const</span> Unsigned &x) {</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(<a class="code" href="namespaceCVC3.html#a1463331d2ef3e7d42ae05802d02271d7">abs</a>(*x.d_n)));</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  }</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span> </div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  Unsigned mod(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  mpz_class r;</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  mpz_mod(r, *x.d_n, *y.d_n);</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">return</span>(Unsigned(Unsigned::Impl(r)));</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  }</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  Unsigned intRoot(<span class="keyword">const</span> Unsigned& base, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> n)</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  {</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(0,1));</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  }</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span> </div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keywordtype">string</span> Unsigned::toString(<span class="keywordtype">int</span> base)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keywordtype">char</span> *tmp = mpz_get_str(NULL, base, *d_n);</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keywordtype">string</span> res(tmp);</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span> <span class="comment">// delete tmp;</span></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  free(tmp);</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="keywordflow">return</span>(res);</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  }</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>  <span class="keywordtype">size_t</span> Unsigned::hash()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <a class="code" href="structHash_1_1hash_3_01const_01char_01_5_01_4.html">std::hash<const char *></a> h;</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keywordflow">return</span> h(toString().c_str());</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  }</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>  <span class="keywordtype">void</span> Unsigned::print()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  cout << (*d_n) << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">endl</a>;</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  }</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span> </div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> </div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span> </div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="comment">// Unary minus</span></div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  Unsigned <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">Unsigned::operator-</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(- (*d_n)));</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  }</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  </div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  Unsigned &Unsigned::operator+=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  *d_n += (*n2.d_n);</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  }</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  </div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  Unsigned &Unsigned::operator-=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  *d_n -= (*n2.d_n);</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keywordflow">return</span> *<span class="keyword">this</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>  </div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  Unsigned &Unsigned::operator*=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  *d_n *= (*n2.d_n);</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  }</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  </div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  Unsigned &Unsigned::operator/=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  *d_n /= (*n2.d_n);</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  }</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>  <span class="keywordtype">int</span> Unsigned::getInt()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordflow">return</span> mpz_get_si(*d_n);</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> </div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Unsigned::getUnsigned()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="keywordflow">return</span> mpz_get_ui(*d_n);</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> </div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a8e164436388f2d87c971d9bbde973c58">operator==</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">return</span>(*n1.d_n == *n2.d_n);</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  }</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#ad3e3964a0b8cd9e2749de47b053b9d97">operator<</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">return</span>(*n1.d_n < *n2.d_n);</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  }</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span> </div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#abccc88aac4f7652def737f1081dc7a89">operator<=</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="keywordflow">return</span>(*n1.d_n <= *n2.d_n);</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  }</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span> </div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a0d82fd3eb68860cbd01ae86b2b9e3c66">operator></a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="keywordflow">return</span>(*n1.d_n > *n2.d_n);</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  }</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>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#af997ba8407b661bf2ffe2cb6f52c3e3b">operator>=</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">return</span>(*n1.d_n >= *n2.d_n);</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  }</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>  <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a5aa953c549c2e103f3834c48bf6cb9a1">operator!=</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">return</span>(*n1.d_n != *n2.d_n);</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  }</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span> </div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  Unsigned <a class="code" href="namespaceCVC3.html#a286cf8699acada708816e72c6b436b90">operator+</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n + *n2.d_n));</div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  }</div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> </div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  Unsigned <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">operator-</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl((*n1.d_n) - (*n2.d_n)));</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  }</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span> </div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  Unsigned <a class="code" href="namespaceCVC3.html#a300bc9244236ebdb1bff90b0b453034c">operator*</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl((*n1.d_n) * (*n2.d_n)));</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  }</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span> </div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  Unsigned <a class="code" href="namespaceCVC3.html#a069aa16342bb9958a3d576a18a390248">operator/</a>(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n / *n2.d_n));</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  }</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span> </div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  Unsigned operator%(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n + *n2.d_n));</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  }</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> }; <span class="comment">/* close namespace */</span></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> </div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span> <span class="preprocessor">#endif</span></div>
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