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<a href="rational-native_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-native.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"> * \brief Implementation of class Rational using native (bounded</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * precision) computer arithmetic</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * Author: Sergey Berezin</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * Created: Mon Jul 28 12:18:03 2003</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * and its documentation for any purpose is hereby granted without</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * LICENSE file provided with this distribution.</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"> * <hr></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"> */</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">/*****************************************************************************/</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#ifdef RATIONAL_NATIVE</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</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="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "<a class="code" href="rational_8h.html">rational.h</a>"</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// For atol() (ASCII to long)</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <stdlib.h></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <limits.h></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include <errno.h></span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include <sstream></span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include <math.h></span></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> <span class="preprocessor">#define OVERFLOW_MSG "\nThis is NOT a bug, but an explicit feature to preserve soundness\nwhen CVC3 uses native computer arithmetic (finite precision). To\navoid these types of errors, please recompile CVC3 with GMP library."</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">namespace </span>CVC3 {</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>  <span class="keyword">using namespace </span>std;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"></span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> //! Add two integers and check for overflows</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> plus(<span class="keywordtype">long</span> <span class="keywordtype">int</span> x, <span class="keywordtype">long</span> <span class="keywordtype">int</span> y) {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> res = x+y;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(((x > 0) != (y > 0)) || ((x > 0) == (res > 0)),</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="stringliteral">"plus(x,y): arithmetic overflow"</span> OVERFLOW_MSG);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">return</span> res;</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> <span class="comment"></span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> //! Add two integers and check for overflows</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> uplus(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> x, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> y) {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> res = x+y;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(res >= x && res >= y,</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="stringliteral">"uplus(x,y): arithmetic overflow"</span> OVERFLOW_MSG);</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">return</span> res;</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> <span class="comment"></span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"> //! Subtract two unsigned integers and check for overflows</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> unsigned_minus(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> x, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> y) {</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> res = x-y;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(res <= x,</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="stringliteral">"unsigned_minus(x,y): arithmetic overflow"</span> OVERFLOW_MSG);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">return</span> res;</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> <span class="comment"></span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"> //! Multiply two unsigned integers and check for overflows</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> umult(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> x, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> y) {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> res = x*y;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(res == 0 || res/x == y,</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="stringliteral">"umult(x,y): arithmetic overflow"</span> OVERFLOW_MSG);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"></span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> //! Shift two unsigned integers and check for overflow</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> ushift(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> x, <span class="keywordtype">unsigned</span> y) {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(y < (<span class="keywordtype">unsigned</span>)numeric_limits<unsigned long>::digits,</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="stringliteral">"ushift(x,y): arithmetic overflow"</span> OVERFLOW_MSG);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> res = (x << y);</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>((res >> y) == x,</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="stringliteral">"ushift(x,y): arithmetic overflow"</span> OVERFLOW_MSG);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">return</span> res;</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"></span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> //! Compute GCD using Euclid's algorithm (from Aaron Stump's code)</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> ugcd(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n1, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n2) {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(n1!=0 && n2!=0,</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="stringliteral">"gcd("</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(n1)+<span class="stringliteral">", "</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(n2)+<span class="stringliteral">"): bad args"</span>);</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">if</span> (n1 < n2) {</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> tmp = n1;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  n1 = n2;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  n2 = tmp;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  }</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>  <span class="comment">// at this point, n1 >= n2</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> r = n1 % n2;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">if</span> (!r)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">return</span> n2;</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>  <span class="keywordflow">return</span> ugcd(n2, r);</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> }</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"></span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"> //! Unary minus which checks for overflows</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> uminus(<span class="keywordtype">long</span> <span class="keywordtype">int</span> x) {</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(x == 0 || x != -x, <span class="stringliteral">"uminus(x): arithmetic overflow"</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  OVERFLOW_MSG);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">return</span> -x;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  }</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"></span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"> //! Multiply two integers and check for overflows</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> mult(<span class="keywordtype">long</span> <span class="keywordtype">int</span> x, <span class="keywordtype">long</span> <span class="keywordtype">int</span> y) {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> res = x*y;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(x==0 || res/x == y, <span class="stringliteral">"mult(x,y): arithmetic overflow"</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  OVERFLOW_MSG);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"></span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> //! Compute GCD using Euclid's algorithm (from Aaron Stump's code)</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> gcd(<span class="keywordtype">long</span> <span class="keywordtype">int</span> n1, <span class="keywordtype">long</span> <span class="keywordtype">int</span> n2) {</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(n1!=0 && n2!=0,</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="stringliteral">"gcd("</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(n1)+<span class="stringliteral">", "</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(n2)+<span class="stringliteral">"): bad args"</span>);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// First, make the arguments positive</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">if</span>(n1 < 0) n1 = uminus(n1);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">if</span>(n2 < 0) n2 = uminus(n2);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">if</span> (n1 < n2) {</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> tmp = n1;</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  n1 = n2;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  n2 = tmp;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  }</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// at this point, n1 >= n2</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> r = n1 % n2;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">if</span> (!r)</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">return</span> n2;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">return</span> gcd(n2, r);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> }</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"></span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> //! Compute LCM</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"></span> <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> lcm(<span class="keywordtype">long</span> <span class="keywordtype">int</span> n1, <span class="keywordtype">long</span> <span class="keywordtype">int</span> n2) {</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> g = gcd(n1,n2);</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">return</span> mult(n1/g, n2);</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> </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ulcm(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n1, <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n2) {</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> g = ugcd(n1,n2);</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">return</span> umult(n1/g, n2);</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> </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="comment">// Implementation of the forward-declared internal class</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keyword">class </span>Rational::Impl {</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> d_num; <span class="comment">//!< Numerator</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"></span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> d_denom; <span class="comment">//!< Denominator</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"></span><span class="comment"> //! Make the rational number canonical</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"></span> <span class="keywordtype">void</span> canonicalize();</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> //! Default Constructor</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"></span> Impl(): d_num(0), d_denom(1) { }<span class="comment"></span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> //! Copy constructor</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"></span> Impl(<span class="keyword">const</span> Impl &x) : d_num(x.d_num), d_denom(x.d_denom) { }<span class="comment"></span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> //! Constructor from unsigned long</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"></span> Impl(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n) :d_num(n), d_denom(1) {</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(d_num >= 0, <span class="stringliteral">"Rational::Impl(unsigned long) - arithmetic overflow"</span>);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  }<span class="comment"></span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment"> //! Constructor from a pair of integers</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment"></span> Impl(<span class="keywordtype">long</span> <span class="keywordtype">int</span> n, <span class="keywordtype">long</span> <span class="keywordtype">int</span> d): d_num(n), d_denom(d) { canonicalize(); }<span class="comment"></span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment"> //! Constructor from a string</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment"></span> Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base);<span class="comment"></span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment"> //! Constructor from a pair of strings</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"></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="l00169"></a><span class="lineno"> 169</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keyword">virtual</span> ~Impl() { }<span class="comment"></span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment"> //! Get numerator</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"></span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> getNum()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> d_num; }<span class="comment"></span></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"> //! Get denominator</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"></span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> getDen()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> d_denom; }</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"></span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment"> //! Unary minus</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"></span> Impl <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">operator-</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment"></span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> //! Equality</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment"></span> <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a8e164436388f2d87c971d9bbde973c58">operator==</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordflow">return</span> (x.d_num == y.d_num && x.d_denom == y.d_denom);</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  }<span class="comment"></span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> //! Dis-equality</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"></span> <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a5aa953c549c2e103f3834c48bf6cb9a1">operator!=</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">return</span> (x.d_num != y.d_num || x.d_denom != y.d_denom);</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  }<span class="comment"></span></div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment"> /*!</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment"> * Compare x=n1/d1 and y=n2/d2 as n1*f2 < n2*f1, where f1=d1/f,</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment"> * f2=d2/f, and f=lcm(d1,d2)</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#ad3e3964a0b8cd9e2749de47b053b9d97">operator<</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  Impl diff(x-y);</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">return</span> diff.d_num < 0;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  }</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#abccc88aac4f7652def737f1081dc7a89">operator<=</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordflow">return</span> (x == y || x < y);</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  }</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> </div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a0d82fd3eb68860cbd01ae86b2b9e3c66">operator></a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  Impl diff(x-y);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordflow">return</span> diff.d_num > 0;</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  }</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#af997ba8407b661bf2ffe2cb6f52c3e3b">operator>=</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">return</span> (x == y || x > y);</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> <span class="comment"></span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"> /*! Addition of x=n1/d1 and y=n2/d2: n1*g2 + n2*g1, where g1=d1/g,</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> * g2=d2/g, and g=lcm(d1,d2)</span></div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#a286cf8699acada708816e72c6b436b90">operator+</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> d1(x.getDen()), d2(y.getDen());</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> f(lcm(d1,d2)), f1(f/d1), f2(f/d2);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n = plus(mult(x.getNum(), f1), mult(y.getNum(), f2));</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">return</span> Impl(n, f);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  }</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">operator-</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba7fa27e82c6c4f69434225ed81e5d151e">TRACE</a>(<span class="stringliteral">"rational"</span>, <span class="stringliteral">"operator-("</span>, x, <span class="stringliteral">", "</span>+y.toString()+<span class="stringliteral">")"</span>);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> d1(x.getDen()), d2(y.getDen());</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> f(lcm(d1,d2)), f1(f/d1), f2(f/d2);</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n = plus(mult(x.getNum(), f1), uminus(mult(y.getNum(), f2)));</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  Impl res(n, f);</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba7fa27e82c6c4f69434225ed81e5d151e">TRACE</a>(<span class="stringliteral">"rational"</span>, <span class="stringliteral">" => "</span>, res, <span class="stringliteral">""</span>);</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">return</span> res;</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> <span class="comment"></span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"> /*!</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"> * Multiplication of x=n1/d1, y=n2/d2:</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"> * (n1/g1)*(n2/g2)/(d1/g2)*(d2/g1), where g1=gcd(n1,d2) and</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment"> * g2=gcd(n2,d1)</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#a300bc9244236ebdb1bff90b0b453034c">operator*</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n1(x.getNum()), d1(x.getDen()), n2(y.getNum()), d2(y.getDen());</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> g1(n1? gcd(n1,d2) : 1), g2(n2? gcd(n2,d1) : 1);</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n(mult(n1/g1, n2/g2)), d(mult(d1/g2, d2/g1));</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">return</span> Impl(n,d);</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> <span class="comment"></span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment"> /*!</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="comment"> * Division of x=n1/d1, y=n2/d2:</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="comment"> * (n1/g1)*(d2/g2)/(d1/g2)*(n2/g1), where g1=gcd(n1,n2) and</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="comment"> * g2=gcd(d1,d2)</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#a069aa16342bb9958a3d576a18a390248">operator/</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n1(x.getNum()), d1(x.getDen()), n2(y.getNum()), d2(y.getDen());</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(n2 != 0, <span class="stringliteral">"Impl::operator/: divisor is 0"</span>);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> g1(n1? gcd(n1,n2) : 1), g2(gcd(d1,d2));</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n(n1? mult(n1/g1, d2/g2) : 0), d(n1? mult(d1/g2, n2/g1) : 1);</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">return</span> Impl(n,d);</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="keyword">friend</span> Impl operator%(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(x.getDen() == 1 && y.getDen() == 1,</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="stringliteral">"Impl % Impl: x and y must be integers"</span>);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">return</span> Impl(x.getNum() % y.getNum(), 1);</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> <span class="comment"></span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment"> //! Print to string</span></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment"></span> <span class="keywordtype">string</span> toString(<span class="keywordtype">int</span> base = 10)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  ostringstream ss;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">if</span> (d_num == 0) ss << <span class="stringliteral">"0"</span>;</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (base == 10) {</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  ss << d_num;</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">if</span> (d_denom != 1)</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  ss << <span class="stringliteral">"/"</span> << d_denom;</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>  <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  vector<int> vec;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="keywordtype">long</span> num = d_num;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">while</span> (num) {</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  vec.push_back(num % base);</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  num = num / base;</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>  <span class="keywordflow">while</span> (!vec.empty()) {</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">if</span> (base > 10 && vec.back() > 10) {</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  ss << (char)(<span class="charliteral">'A'</span> + (vec.back()-10));</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>  <span class="keywordflow">else</span> ss << vec.back();</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  vec.pop_back();</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  }</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordflow">if</span>(d_denom != 1) {</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  ss << <span class="stringliteral">"/"</span>;</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keywordflow">if</span> (d_denom == 0) ss << <span class="stringliteral">"0"</span>;</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  num = d_denom;</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">while</span> (num) {</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  vec.push_back(num % base);</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  num = num / base;</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  }</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keywordflow">while</span> (!vec.empty()) {</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordflow">if</span> (base > 10 && vec.back() > 10) {</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  ss << (char)(<span class="charliteral">'A'</span> + (vec.back()-10));</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  }</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">else</span> ss << vec.back();</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  vec.pop_back();</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  }</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  }</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>  }</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordflow">return</span>(ss.str());</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> <span class="comment"></span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="comment"> //! Printing to ostream</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment"></span> <span class="keyword">friend</span> ostream& <a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(ostream& os, <span class="keyword">const</span> Rational::Impl& n) {</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">return</span> os << n.toString();</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  }</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </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="comment">// Make the rational number canonical</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordtype">void</span> Rational::Impl::canonicalize() {</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(d_denom != 0,</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="stringliteral">"Rational::Impl::canonicalize: bad denominator: "</span></div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  +<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(d_denom));</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">if</span>(d_num == 0) {</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  d_denom = 1;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordflow">if</span>(d_denom < 0) {</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  d_num = uminus(d_num);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  d_denom = uminus(d_denom);</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">long</span> <span class="keywordtype">int</span> d = gcd(d_num, d_denom);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordflow">if</span>(d != 1) {</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  d_num /= d;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  d_denom /= d;</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  }</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  }</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>  <span class="comment">// Constructor from a string</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  Rational::Impl::Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base) {</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordtype">size_t</span> i, iend;</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordflow">for</span>(i=0,iend=n.size(); i<iend && n[i] != <span class="charliteral">'/'</span>; ++i);</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">if</span>(i<iend)</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="comment">// Found slash at i</span></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  *<span class="keyword">this</span> = Impl(n.substr(0,i-1), n.substr(i+1,iend-1), base);</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  *<span class="keyword">this</span> = Impl(n, <span class="stringliteral">"1"</span>, base);</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  canonicalize();</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>  <span class="comment">// Constructor from a pair of strings</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  Rational::Impl::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="l00345"></a><span class="lineno"> 345</span>  d_num = strtol(n.c_str(), NULL, base);</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(d_num != LONG_MIN && d_num != LONG_MAX,</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="stringliteral">"Rational::Impl(string, string): arithmetic overflow:"</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="stringliteral">"n = "</span>+n+<span class="stringliteral">", d="</span>+d+<span class="stringliteral">", base="</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(base)</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  +OVERFLOW_MSG);</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  d_denom = strtol(d.c_str(), NULL, base);</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(d_denom != LONG_MIN && d_denom != LONG_MAX,</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="stringliteral">"Rational::Impl(string, string): arithmetic overflow:"</span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="stringliteral">"n = "</span>+n+<span class="stringliteral">", d="</span>+d+<span class="stringliteral">", base="</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(base)</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  +OVERFLOW_MSG);</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  canonicalize();</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  }</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>  Rational::Impl <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">Rational::Impl::operator-</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordflow">return</span> Impl(uminus(d_num), d_denom);</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  }</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="comment"></span></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment"> //! Default constructor</span></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html#a8f86f975b54d0a491bc909d677023467">Rational::Rational</a>() : d_n(new Impl) {</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  num_created++;</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  printStats();</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="preprocessor"></span> }<span class="comment"></span></div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> <span class="comment"> //! Copy constructor</span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> <span class="comment"></span> Rational::Rational(<span class="keyword">const</span> Rational &n) : d_n(new Impl(*n.d_n)) {</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  num_created++;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  printStats();</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> <span class="preprocessor"></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>  Rational::Rational(<span class="keyword">const</span> Unsigned &n) : d_n(new Impl(n.getUnsigned())) {</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  num_created++;</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  printStats();</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="comment"></span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="comment"> //! Private constructor</span></div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="comment"></span> Rational::Rational(<span class="keyword">const</span> Impl& t): d_n(new Impl(t)) {</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  num_created++;</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  printStats();</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</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="l00397"></a><span class="lineno"> 397</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  num_created++;</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  printStats();</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="comment">// Constructors from strings</span></div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</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="l00405"></a><span class="lineno"> 405</span>  : d_n(new Impl(string(n), base)) {</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  num_created++;</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  printStats();</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</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="l00413"></a><span class="lineno"> 413</span>  : d_n(new Impl(n, base)) {</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  num_created++;</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  printStats();</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</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="l00421"></a><span class="lineno"> 421</span>  : d_n(new Impl(string(n), string(d), base)) {</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  num_created++;</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  printStats();</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</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="l00429"></a><span class="lineno"> 429</span>  : d_n(new Impl(n, d, base)) {</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  num_created++;</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  printStats();</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="preprocessor"></span> }</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  Rational::~Rational() {</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keyword">delete</span> d_n;</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> &num_deleted = getDeleted();</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  num_deleted++;</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  printStats();</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span> <span class="preprocessor"></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>  <span class="comment">// Get components</span></div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  Rational Rational::getNumerator()<span class="keyword"> const</span></div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span> <span class="keyword"> </span>{ <span class="keywordflow">return</span> Rational(Impl(d_n->getNum(), 1)); }</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  Rational Rational::getDenominator()<span class="keyword"> const</span></div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="keyword"> </span>{ <span class="keywordflow">return</span> Rational(Impl(d_n->getDen(), 1)); }</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>  <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="l00453"></a><span class="lineno"> 453</span> </div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="comment">// Assignment</span></div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  Rational& Rational::operator=(<span class="keyword">const</span> Rational& n) {</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</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="l00457"></a><span class="lineno"> 457</span>  <span class="keyword">delete</span> d_n;</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  d_n = <span class="keyword">new</span> Impl(*n.d_n);</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keywordflow">return</span> *<span class="keyword">this</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> </div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</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="l00463"></a><span class="lineno"> 463</span>  <span class="keywordflow">return</span>(os << n.toString());</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> </div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="comment">// Check that argument is an int and print an error message otherwise</span></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>  <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="l00470"></a><span class="lineno"> 470</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(n.isInteger(),</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  (<span class="stringliteral">"CVC3::Rational::"</span> + funName</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  + <span class="stringliteral">": argument is not an integer: "</span> + n.toString()).c_str());</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>  <span class="comment">/* Computes gcd and lcm on *integer* values. Result is always a</span></div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="comment"> positive integer. In this implementation, it is guaranteed by</span></div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> <span class="comment"> GMP. */</span></div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span> </div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  Rational gcd(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  checkInt(x, <span class="stringliteral">"gcd(*x*,y)"</span>);</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  checkInt(y, <span class="stringliteral">"gcd(x,*y*)"</span>);</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(gcd(x.d_n->getNum(), y.d_n->getNum()), 1));</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</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>  Rational gcd(<span class="keyword">const</span> vector<Rational> &v) {</div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> g(1);</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keywordflow">if</span>(v.size() > 0) {</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  checkInt(v[0], <span class="stringliteral">"gcd(vector<Rational>[0])"</span>);</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  g = v[0].d_n->getNum();</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>  <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i=1; i<v.size(); i++) {</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  checkInt(v[i], <span class="stringliteral">"gcd(vector<Rational>)"</span>);</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keywordflow">if</span>(g == 0) g = v[i].d_n->getNum();</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(v[i].d_n->getNum() != 0)</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  g = gcd(g, v[i].d_n->getNum());</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>  <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</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>  Rational lcm(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> g;</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  checkInt(x, <span class="stringliteral">"lcm(*x*,y)"</span>);</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  checkInt(y, <span class="stringliteral">"lcm(x,*y*)"</span>);</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  g = lcm(x.d_n->getNum(), y.d_n->getNum());</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(g, 1));</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  }</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>  Rational lcm(<span class="keyword">const</span> vector<Rational> &v) {</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> g(1);</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i=0; i<v.size(); i++) {</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  checkInt(v[i], <span class="stringliteral">"lcm(vector<Rational>)"</span>);</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="keywordflow">if</span>(v[i].d_n->getNum() != 0)</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  g = lcm(g, v[i].d_n->getNum());</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>  <span class="keywordflow">return</span> Rational(Rational::Impl(g,1));</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> </div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  Rational <a class="code" href="namespaceCVC3.html#a1463331d2ef3e7d42ae05802d02271d7">abs</a>(<span class="keyword">const</span> Rational &x) {</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n(x.d_n->getNum());</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="keywordflow">if</span>(n>=0) <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(-n, x.d_n->getDen()));</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  }</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>  Rational floor(<span class="keyword">const</span> Rational &x) {</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="keywordflow">if</span>(x.d_n->getDen() == 1) <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n = x.d_n->getNum();</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> nAbs = (n<0)? uminus(n) : n;</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> q = nAbs / x.d_n->getDen();</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="keywordflow">if</span>(n < 0) q = plus(uminus(q), -1);</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(q,1));</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>  Rational ceil(<span class="keyword">const</span> Rational &x) {</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="keywordflow">if</span>(x.d_n->getDen() == 1) <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> n = x.d_n->getNum();</div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> nAbs = (n<0)? -n : n;</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> q = nAbs / x.d_n->getDen();</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="keywordflow">if</span>(n > 0) q = plus(q, 1);</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="keywordflow">else</span> q = uminus(q);</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(q,1));</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  }</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> </div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  Rational mod(<span class="keyword">const</span> Rational &x, <span class="keyword">const</span> Rational &y) {</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  checkInt(x, <span class="stringliteral">"mod(*x*,y)"</span>);</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  checkInt(y, <span class="stringliteral">"mod(x,*y*)"</span>);</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> r = x.d_n->getNum() % y.d_n->getNum();</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  <span class="keywordflow">return</span>(Rational(Rational::Impl(r,1)));</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> </div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</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="l00551"></a><span class="lineno"> 551</span>  checkInt(base, <span class="stringliteral">"intRoot(*x*,y)"</span>);</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  checkInt(n, <span class="stringliteral">"intRoot(x,*y*)"</span>);</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <span class="keywordtype">double</span> b = base.d_n->getNum();</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="keywordtype">double</span> root = n;</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  root = 1/root;</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  b = <a class="code" href="namespaceCVC3.html#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">::pow</a>(b, root);</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="keywordtype">long</span> res = (long) ::floor(b);</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="keywordflow">if</span> (::<a class="code" href="namespaceCVC3.html#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">pow</a>((<span class="keywordtype">long</span> <span class="keywordtype">double</span>)res, (<span class="keywordtype">int</span>)n) == base.<a class="code" href="classCVC3_1_1Rational.html#a704e9a119182f45ca64d5899f683f17a">d_n</a>->getNum()) {</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(res,1));</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  }</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="keywordflow">return</span> Rational(Rational::Impl((<span class="keywordtype">long</span>)0,(<span class="keywordtype">long</span>)1));</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  }</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span> </div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</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="l00565"></a><span class="lineno"> 565</span>  <span class="keywordflow">return</span>(d_n->toString(base));</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  }</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="keywordtype">size_t</span> Rational::hash()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</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="l00570"></a><span class="lineno"> 570</span>  <span class="keywordflow">return</span> h(toString().c_str());</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  }</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span> </div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  <span class="keywordtype">void</span> Rational::print()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  cout << (*this) << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">endl</a>;</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  }</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span> </div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  <span class="comment">// Unary minus</span></div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  Rational <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">Rational::operator-</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(-(d_n->getNum()), d_n->getDen()));</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  }</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span> </div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  Rational &Rational::operator+=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  *<span class="keyword">this</span> = (*this) + n2;</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  }</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span> </div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  Rational &Rational::operator-=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  *<span class="keyword">this</span> = (*this) - n2;</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  }</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span> </div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  Rational &Rational::operator*=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  *<span class="keyword">this</span> = (*this) * n2;</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  }</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span> </div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  Rational &Rational::operator/=(<span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  *<span class="keyword">this</span> = (*this) / n2;</div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  }</div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span> </div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  <span class="keywordtype">int</span> Rational::getInt()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  checkInt(*<span class="keyword">this</span>, <span class="stringliteral">"getInt()"</span>);</div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> res = d_n->getNum();</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(res >= INT_MIN && res <= INT_MAX,</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="stringliteral">"Rational::getInt(): arithmetic overflow on "</span>+toString() +</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  OVERFLOW_MSG);</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  <span class="keywordflow">return</span> (<span class="keywordtype">int</span>)res;</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  }</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span> </div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Rational::getUnsigned()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  checkInt(*<span class="keyword">this</span>, <span class="stringliteral">"getUnsigned()"</span>);</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> res = d_n->getNum();</div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(res >= 0 && res <= (<span class="keywordtype">long</span> <span class="keywordtype">int</span>)UINT_MAX,</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <span class="stringliteral">"Rational::getUnsigned(): arithmetic overflow on "</span> + toString() +</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  OVERFLOW_MSG);</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <span class="keywordflow">return</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>)res;</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  }</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span> </div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span> <span class="preprocessor">#ifdef _DEBUG_RATIONAL_</span></div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span> <span class="preprocessor"></span> <span class="keywordtype">void</span> Rational::printStats() {</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  <span class="keywordtype">int</span> &num_created = getCreated();</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <span class="keywordtype">int</span> &num_deleted = getDeleted();</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="keywordflow">if</span>(num_created % 1000 == 0 || num_deleted % 1000 == 0) {</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  std::cerr << <span class="stringliteral">"Rational("</span> << *d_n << <span class="stringliteral">"): created "</span> << num_created</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  << <span class="stringliteral">", deleted "</span> << num_deleted</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  << <span class="stringliteral">", currently alive "</span> << num_created-num_deleted</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</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="l00629"></a><span class="lineno"> 629</span>  }</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  }</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</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="l00634"></a><span class="lineno"> 634</span>  <span class="keywordflow">return</span>(*n1.d_n == *n2.d_n);</div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  }</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span> </div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</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="l00638"></a><span class="lineno"> 638</span>  <span class="keywordflow">return</span>(*n1.d_n < *n2.d_n);</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  }</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span> </div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</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="l00642"></a><span class="lineno"> 642</span>  <span class="keywordflow">return</span>(*n1.d_n <= *n2.d_n);</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  }</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span> </div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</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="l00646"></a><span class="lineno"> 646</span>  <span class="keywordflow">return</span>(*n1.d_n > *n2.d_n);</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  }</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span> </div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</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="l00650"></a><span class="lineno"> 650</span>  <span class="keywordflow">return</span>(*n1.d_n >= *n2.d_n);</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  }</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span> </div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</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="l00654"></a><span class="lineno"> 654</span>  <span class="keywordflow">return</span>(*n1.d_n != *n2.d_n);</div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  }</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span> </div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</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="l00658"></a><span class="lineno"> 658</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n + *n2.d_n));</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  }</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span> </div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</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="l00662"></a><span class="lineno"> 662</span>  <span class="keywordflow">return</span> Rational(Rational::Impl((*n1.d_n) - (*n2.d_n)));</div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  }</div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span> </div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</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="l00666"></a><span class="lineno"> 666</span>  <span class="keywordflow">return</span> Rational(Rational::Impl((*n1.d_n) * (*n2.d_n)));</div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  }</div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span> </div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</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="l00670"></a><span class="lineno"> 670</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n / *n2.d_n));</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  }</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span> </div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  Rational operator%(<span class="keyword">const</span> Rational &n1, <span class="keyword">const</span> Rational &n2) {</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keywordflow">return</span> Rational(Rational::Impl(*n1.d_n % *n2.d_n));</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  }</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span> </div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  <span class="comment">// Implementation of the forward-declared internal class</span></div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  <span class="keyword">class </span>Unsigned::Impl {</div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> d_num;</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  <span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span> <span class="comment"> //! Default Constructor</span></div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span> <span class="comment"></span> Impl(): d_num(0) { }<span class="comment"></span></div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span> <span class="comment"> //! Copy constructor</span></div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span> <span class="comment"></span> Impl(<span class="keyword">const</span> Impl &x) : d_num(x.d_num) { }<span class="comment"></span></div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span> <span class="comment"> //! Constructor from an unsigned integer</span></div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span> <span class="comment"></span> Impl(<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n): d_num(n) { }<span class="comment"></span></div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span> <span class="comment"> //! Constructor from an int</span></div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span> <span class="comment"></span> Impl(<span class="keywordtype">int</span> n): d_num(n) {</div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(n >= 0, <span class="stringliteral">"Attempt to create Unsigned from negative integer"</span>);</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  }</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span> <span class="comment"></span></div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span> <span class="comment"> //! Constructor from a string</span></div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span> <span class="comment"></span> Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base);</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  <span class="keyword">virtual</span> ~Impl() { }<span class="comment"></span></div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span> <span class="comment"> //! Get unsigned</span></div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span> <span class="comment"></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> getUnsigned()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> d_num; }</div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span> </div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span> <span class="comment"></span></div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span> <span class="comment"> //! Equality</span></div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span> <span class="comment"></span> <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a8e164436388f2d87c971d9bbde973c58">operator==</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="keywordflow">return</span> (x.d_num == y.d_num);</div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  }<span class="comment"></span></div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span> <span class="comment"> //! Dis-equality</span></div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span> <span class="comment"></span> <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a5aa953c549c2e103f3834c48bf6cb9a1">operator!=</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <span class="keywordflow">return</span> (x.d_num != y.d_num);</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  }</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#ad3e3964a0b8cd9e2749de47b053b9d97">operator<</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="keywordflow">return</span> x.d_num < y.d_num;</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  }</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span> </div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#abccc88aac4f7652def737f1081dc7a89">operator<=</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  <span class="keywordflow">return</span> (x.d_num <= y.d_num);</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  }</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span> </div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a0d82fd3eb68860cbd01ae86b2b9e3c66">operator></a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <span class="keywordflow">return</span> x.d_num > y.d_num;</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  }</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span> </div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  <span class="keyword">friend</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#af997ba8407b661bf2ffe2cb6f52c3e3b">operator>=</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  <span class="keywordflow">return</span> x.d_num >= y.d_num;</div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  }</div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span> </div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#a286cf8699acada708816e72c6b436b90">operator+</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  <span class="keywordflow">return</span> Impl(uplus(x.d_num, y.d_num));</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  }</div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span> </div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#aacf567dce1c762f957267427472bd959">operator-</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n = unsigned_minus(x.d_num, y.d_num);</div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  Impl res(n);</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  }</div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span> </div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#a300bc9244236ebdb1bff90b0b453034c">operator*</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n(umult(x.d_num, y.d_num));</div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  <span class="keywordflow">return</span> Impl(n);</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  }</div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span> </div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#a069aa16342bb9958a3d576a18a390248">operator/</a>(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(y.d_num != 0, <span class="stringliteral">"Impl::operator/: divisor is 0"</span>);</div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n(x.d_num / y.d_num);</div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  <span class="keywordflow">return</span> Impl(n);</div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  }</div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span> </div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  <span class="keyword">friend</span> Impl operator%(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(y.d_num != 0,</div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  <span class="stringliteral">"Impl % Impl: y must be non-zero"</span>);</div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  <span class="keywordflow">return</span> Impl(x.d_num % y.d_num);</div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  }</div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span> </div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  <span class="keyword">friend</span> Impl <a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(<span class="keyword">const</span> Impl& x, <span class="keywordtype">unsigned</span> y) {</div>
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> n(ushift(x.d_num, y));</div>
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  <span class="keywordflow">return</span> Impl(n);</div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  }</div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span> </div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <span class="keyword">friend</span> Impl operator&(<span class="keyword">const</span> Impl& x, <span class="keyword">const</span> Impl& y) {</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  <span class="keywordflow">return</span> Impl(x.d_num & y.d_num);</div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  }</div>
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span> <span class="comment"></span></div>
<div class="line"><a name="l00760"></a><span class="lineno"> 760</span> <span class="comment"> //! Print to string</span></div>
<div class="line"><a name="l00761"></a><span class="lineno"> 761</span> <span class="comment"></span> <span class="keywordtype">string</span> toString(<span class="keywordtype">int</span> base = 10)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  ostringstream ss;</div>
<div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  <span class="keywordflow">if</span> (d_num == 0) ss << <span class="stringliteral">"0"</span>;</div>
<div class="line"><a name="l00764"></a><span class="lineno"> 764</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (base == 10) {</div>
<div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  ss << d_num;</div>
<div class="line"><a name="l00766"></a><span class="lineno"> 766</span>  }</div>
<div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  vector<int> vec;</div>
<div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  <span class="keywordtype">long</span> num = d_num;</div>
<div class="line"><a name="l00770"></a><span class="lineno"> 770</span>  <span class="keywordflow">while</span> (num) {</div>
<div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  vec.push_back(num % base);</div>
<div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  num = num / base;</div>
<div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  }</div>
<div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  <span class="keywordflow">while</span> (!vec.empty()) {</div>
<div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  <span class="keywordflow">if</span> (base > 10 && vec.back() > 10) {</div>
<div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  ss << (char)(<span class="charliteral">'A'</span> + (vec.back()-10));</div>
<div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  }</div>
<div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  <span class="keywordflow">else</span> ss << vec.back();</div>
<div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  vec.pop_back();</div>
<div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  }</div>
<div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  }</div>
<div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  <span class="keywordflow">return</span>(ss.str());</div>
<div class="line"><a name="l00783"></a><span class="lineno"> 783</span>  }</div>
<div class="line"><a name="l00784"></a><span class="lineno"> 784</span> <span class="comment"></span></div>
<div class="line"><a name="l00785"></a><span class="lineno"> 785</span> <span class="comment"> //! Printing to ostream</span></div>
<div class="line"><a name="l00786"></a><span class="lineno"> 786</span> <span class="comment"></span> <span class="keyword">friend</span> ostream& <a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(ostream& os, <span class="keyword">const</span> Unsigned::Impl& n) {</div>
<div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  <span class="keywordflow">return</span> os << n.toString();</div>
<div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  }</div>
<div class="line"><a name="l00789"></a><span class="lineno"> 789</span> </div>
<div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  };</div>
<div class="line"><a name="l00791"></a><span class="lineno"> 791</span> </div>
<div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  <span class="comment">// Constructor from a pair of strings</span></div>
<div class="line"><a name="l00793"></a><span class="lineno"> 793</span>  Unsigned::Impl::Impl(<span class="keyword">const</span> <span class="keywordtype">string</span> &n, <span class="keywordtype">int</span> base) {</div>
<div class="line"><a name="l00794"></a><span class="lineno"> 794</span>  d_num = strtoul(n.c_str(), NULL, base);</div>
<div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(d_num != ULONG_MAX,</div>
<div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  <span class="stringliteral">"Unsigned::Impl(string): arithmetic overflow:"</span></div>
<div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  <span class="stringliteral">"n = "</span>+n+<span class="stringliteral">", base="</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(base)</div>
<div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  +OVERFLOW_MSG);</div>
<div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  }</div>
<div class="line"><a name="l00800"></a><span class="lineno"> 800</span> <span class="comment"></span></div>
<div class="line"><a name="l00801"></a><span class="lineno"> 801</span> <span class="comment"> //! Default constructor</span></div>
<div class="line"><a name="l00802"></a><span class="lineno"> 802</span> <span class="comment"></span> Unsigned::Unsigned() : d_n(new Impl) { }<span class="comment"></span></div>
<div class="line"><a name="l00803"></a><span class="lineno"> 803</span> <span class="comment"> //! Copy constructor</span></div>
<div class="line"><a name="l00804"></a><span class="lineno"> 804</span> <span class="comment"></span> Unsigned::Unsigned(<span class="keyword">const</span> Unsigned &n) : d_n(new Impl(*n.d_n)) { }</div>
<div class="line"><a name="l00805"></a><span class="lineno"> 805</span> <span class="comment"></span></div>
<div class="line"><a name="l00806"></a><span class="lineno"> 806</span> <span class="comment"> //! Private constructor</span></div>
<div class="line"><a name="l00807"></a><span class="lineno"> 807</span> <span class="comment"></span> Unsigned::Unsigned(<span class="keyword">const</span> Impl& t): d_n(new Impl(t)) { }</div>
<div class="line"><a name="l00808"></a><span class="lineno"> 808</span> </div>
<div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  Unsigned::Unsigned(<span class="keywordtype">unsigned</span> n): d_n(new Impl((unsigned long)n)) { }</div>
<div class="line"><a name="l00810"></a><span class="lineno"> 810</span>  Unsigned::Unsigned(<span class="keywordtype">int</span> n): d_n(new Impl(n)) { }</div>
<div class="line"><a name="l00811"></a><span class="lineno"> 811</span> </div>
<div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  <span class="comment">// Constructors from strings</span></div>
<div class="line"><a name="l00813"></a><span class="lineno"> 813</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="l00814"></a><span class="lineno"> 814</span>  : d_n(new Impl(string(n), base)) { }</div>
<div class="line"><a name="l00815"></a><span class="lineno"> 815</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="l00816"></a><span class="lineno"> 816</span>  : d_n(new Impl(n, base)) { }</div>
<div class="line"><a name="l00817"></a><span class="lineno"> 817</span> </div>
<div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  Unsigned::~Unsigned() {</div>
<div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  <span class="keyword">delete</span> d_n;</div>
<div class="line"><a name="l00821"></a><span class="lineno"> 821</span>  }</div>
<div class="line"><a name="l00822"></a><span class="lineno"> 822</span> </div>
<div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  <span class="comment">// Assignment</span></div>
<div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  Unsigned& Unsigned::operator=(<span class="keyword">const</span> Unsigned& n) {</div>
<div class="line"><a name="l00825"></a><span class="lineno"> 825</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="l00826"></a><span class="lineno"> 826</span>  <span class="keyword">delete</span> d_n;</div>
<div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  d_n = <span class="keyword">new</span> Impl(*n.d_n);</div>
<div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  }</div>
<div class="line"><a name="l00830"></a><span class="lineno"> 830</span> </div>
<div class="line"><a name="l00831"></a><span class="lineno"> 831</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="l00832"></a><span class="lineno"> 832</span>  <span class="keywordflow">return</span>(os << n.toString());</div>
<div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  }</div>
<div class="line"><a name="l00834"></a><span class="lineno"> 834</span> </div>
<div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  Unsigned gcd(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {</div>
<div class="line"><a name="l00836"></a><span class="lineno"> 836</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(ugcd(x.d_n->getUnsigned(), y.d_n->getUnsigned())));</div>
<div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  }</div>
<div class="line"><a name="l00838"></a><span class="lineno"> 838</span> </div>
<div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  Unsigned gcd(<span class="keyword">const</span> vector<Unsigned> &v) {</div>
<div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> g(1);</div>
<div class="line"><a name="l00841"></a><span class="lineno"> 841</span>  <span class="keywordflow">if</span>(v.size() > 0) {</div>
<div class="line"><a name="l00842"></a><span class="lineno"> 842</span>  g = v[0].d_n->getUnsigned();</div>
<div class="line"><a name="l00843"></a><span class="lineno"> 843</span>  }</div>
<div class="line"><a name="l00844"></a><span class="lineno"> 844</span>  <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i=1; i<v.size(); i++) {</div>
<div class="line"><a name="l00845"></a><span class="lineno"> 845</span>  <span class="keywordflow">if</span>(g == 0) g = v[i].d_n->getUnsigned();</div>
<div class="line"><a name="l00846"></a><span class="lineno"> 846</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(v[i].d_n->getUnsigned() != 0)</div>
<div class="line"><a name="l00847"></a><span class="lineno"> 847</span>  g = ugcd(g, v[i].d_n->getUnsigned());</div>
<div class="line"><a name="l00848"></a><span class="lineno"> 848</span>  }</div>
<div class="line"><a name="l00849"></a><span class="lineno"> 849</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));</div>
<div class="line"><a name="l00850"></a><span class="lineno"> 850</span>  }</div>
<div class="line"><a name="l00851"></a><span class="lineno"> 851</span> </div>
<div class="line"><a name="l00852"></a><span class="lineno"> 852</span>  Unsigned lcm(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {</div>
<div class="line"><a name="l00853"></a><span class="lineno"> 853</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> g;</div>
<div class="line"><a name="l00854"></a><span class="lineno"> 854</span>  g = ulcm(x.d_n->getUnsigned(), y.d_n->getUnsigned());</div>
<div class="line"><a name="l00855"></a><span class="lineno"> 855</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));</div>
<div class="line"><a name="l00856"></a><span class="lineno"> 856</span>  }</div>
<div class="line"><a name="l00857"></a><span class="lineno"> 857</span> </div>
<div class="line"><a name="l00858"></a><span class="lineno"> 858</span>  Unsigned lcm(<span class="keyword">const</span> vector<Unsigned> &v) {</div>
<div class="line"><a name="l00859"></a><span class="lineno"> 859</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> g(1);</div>
<div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i=0; i<v.size(); i++) {</div>
<div class="line"><a name="l00861"></a><span class="lineno"> 861</span>  <span class="keywordflow">if</span>(v[i].d_n->getUnsigned() != 0)</div>
<div class="line"><a name="l00862"></a><span class="lineno"> 862</span>  g = ulcm(g, v[i].d_n->getUnsigned());</div>
<div class="line"><a name="l00863"></a><span class="lineno"> 863</span>  }</div>
<div class="line"><a name="l00864"></a><span class="lineno"> 864</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(g));</div>
<div class="line"><a name="l00865"></a><span class="lineno"> 865</span>  }</div>
<div class="line"><a name="l00866"></a><span class="lineno"> 866</span> </div>
<div class="line"><a name="l00867"></a><span class="lineno"> 867</span>  Unsigned mod(<span class="keyword">const</span> Unsigned &x, <span class="keyword">const</span> Unsigned &y) {</div>
<div class="line"><a name="l00868"></a><span class="lineno"> 868</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> r = x.d_n->getUnsigned() % y.d_n->getUnsigned();</div>
<div class="line"><a name="l00869"></a><span class="lineno"> 869</span>  <span class="keywordflow">return</span>(Unsigned(Unsigned::Impl(r)));</div>
<div class="line"><a name="l00870"></a><span class="lineno"> 870</span>  }</div>
<div class="line"><a name="l00871"></a><span class="lineno"> 871</span> </div>
<div class="line"><a name="l00872"></a><span class="lineno"> 872</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="l00873"></a><span class="lineno"> 873</span>  <span class="keywordtype">double</span> b = base.d_n->getUnsigned();</div>
<div class="line"><a name="l00874"></a><span class="lineno"> 874</span>  <span class="keywordtype">double</span> root = n;</div>
<div class="line"><a name="l00875"></a><span class="lineno"> 875</span>  root = 1/root;</div>
<div class="line"><a name="l00876"></a><span class="lineno"> 876</span>  b = <a class="code" href="namespaceCVC3.html#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">::pow</a>(b, root);</div>
<div class="line"><a name="l00877"></a><span class="lineno"> 877</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> res = (<span class="keywordtype">unsigned</span> long) ::floor(b);</div>
<div class="line"><a name="l00878"></a><span class="lineno"> 878</span>  <span class="keywordflow">if</span> (::<a class="code" href="namespaceCVC3.html#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">pow</a>((<span class="keywordtype">long</span> <span class="keywordtype">double</span>)res, (<span class="keywordtype">int</span>)n) == base.<a class="code" href="classCVC3_1_1Rational.html#a704e9a119182f45ca64d5899f683f17a">d_n</a>->getUnsigned()) {</div>
<div class="line"><a name="l00879"></a><span class="lineno"> 879</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(res));</div>
<div class="line"><a name="l00880"></a><span class="lineno"> 880</span>  }</div>
<div class="line"><a name="l00881"></a><span class="lineno"> 881</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl((<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span>)0));</div>
<div class="line"><a name="l00882"></a><span class="lineno"> 882</span>  }</div>
<div class="line"><a name="l00883"></a><span class="lineno"> 883</span> </div>
<div class="line"><a name="l00884"></a><span class="lineno"> 884</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="l00885"></a><span class="lineno"> 885</span>  <span class="keywordflow">return</span>(d_n->toString(base));</div>
<div class="line"><a name="l00886"></a><span class="lineno"> 886</span>  }</div>
<div class="line"><a name="l00887"></a><span class="lineno"> 887</span> </div>
<div class="line"><a name="l00888"></a><span class="lineno"> 888</span>  <span class="keywordtype">size_t</span> Unsigned::hash()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00889"></a><span class="lineno"> 889</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="l00890"></a><span class="lineno"> 890</span>  <span class="keywordflow">return</span> h(toString().c_str());</div>
<div class="line"><a name="l00891"></a><span class="lineno"> 891</span>  }</div>
<div class="line"><a name="l00892"></a><span class="lineno"> 892</span> </div>
<div class="line"><a name="l00893"></a><span class="lineno"> 893</span>  <span class="keywordtype">void</span> Unsigned::print()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00894"></a><span class="lineno"> 894</span>  cout << (*this) << <a class="code" href="group__ExprStream__Manip.html#ga05b0ea7353ec24fa8e7e272d7a7875d8" title="Print the end-of-line.">endl</a>;</div>
<div class="line"><a name="l00895"></a><span class="lineno"> 895</span>  }</div>
<div class="line"><a name="l00896"></a><span class="lineno"> 896</span> </div>
<div class="line"><a name="l00897"></a><span class="lineno"> 897</span>  Unsigned &Unsigned::operator+=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00898"></a><span class="lineno"> 898</span>  *<span class="keyword">this</span> = (*this) + n2;</div>
<div class="line"><a name="l00899"></a><span class="lineno"> 899</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00900"></a><span class="lineno"> 900</span>  }</div>
<div class="line"><a name="l00901"></a><span class="lineno"> 901</span> </div>
<div class="line"><a name="l00902"></a><span class="lineno"> 902</span>  Unsigned &Unsigned::operator-=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00903"></a><span class="lineno"> 903</span>  *<span class="keyword">this</span> = (*this) - n2;</div>
<div class="line"><a name="l00904"></a><span class="lineno"> 904</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00905"></a><span class="lineno"> 905</span>  }</div>
<div class="line"><a name="l00906"></a><span class="lineno"> 906</span> </div>
<div class="line"><a name="l00907"></a><span class="lineno"> 907</span>  Unsigned &Unsigned::operator*=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00908"></a><span class="lineno"> 908</span>  *<span class="keyword">this</span> = (*this) * n2;</div>
<div class="line"><a name="l00909"></a><span class="lineno"> 909</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00910"></a><span class="lineno"> 910</span>  }</div>
<div class="line"><a name="l00911"></a><span class="lineno"> 911</span> </div>
<div class="line"><a name="l00912"></a><span class="lineno"> 912</span>  Unsigned &Unsigned::operator/=(<span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00913"></a><span class="lineno"> 913</span>  *<span class="keyword">this</span> = (*this) / n2;</div>
<div class="line"><a name="l00914"></a><span class="lineno"> 914</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00915"></a><span class="lineno"> 915</span>  }</div>
<div class="line"><a name="l00916"></a><span class="lineno"> 916</span> </div>
<div class="line"><a name="l00917"></a><span class="lineno"> 917</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> Unsigned::getUnsigned()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00918"></a><span class="lineno"> 918</span>  <span class="keywordflow">return</span> d_n->getUnsigned();</div>
<div class="line"><a name="l00919"></a><span class="lineno"> 919</span>  }</div>
<div class="line"><a name="l00920"></a><span class="lineno"> 920</span> </div>
<div class="line"><a name="l00921"></a><span class="lineno"> 921</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="l00922"></a><span class="lineno"> 922</span>  <span class="keywordflow">return</span>(*n1.d_n == *n2.d_n);</div>
<div class="line"><a name="l00923"></a><span class="lineno"> 923</span>  }</div>
<div class="line"><a name="l00924"></a><span class="lineno"> 924</span> </div>
<div class="line"><a name="l00925"></a><span class="lineno"> 925</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="l00926"></a><span class="lineno"> 926</span>  <span class="keywordflow">return</span>(*n1.d_n < *n2.d_n);</div>
<div class="line"><a name="l00927"></a><span class="lineno"> 927</span>  }</div>
<div class="line"><a name="l00928"></a><span class="lineno"> 928</span> </div>
<div class="line"><a name="l00929"></a><span class="lineno"> 929</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="l00930"></a><span class="lineno"> 930</span>  <span class="keywordflow">return</span>(*n1.d_n <= *n2.d_n);</div>
<div class="line"><a name="l00931"></a><span class="lineno"> 931</span>  }</div>
<div class="line"><a name="l00932"></a><span class="lineno"> 932</span> </div>
<div class="line"><a name="l00933"></a><span class="lineno"> 933</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="l00934"></a><span class="lineno"> 934</span>  <span class="keywordflow">return</span>(*n1.d_n > *n2.d_n);</div>
<div class="line"><a name="l00935"></a><span class="lineno"> 935</span>  }</div>
<div class="line"><a name="l00936"></a><span class="lineno"> 936</span> </div>
<div class="line"><a name="l00937"></a><span class="lineno"> 937</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="l00938"></a><span class="lineno"> 938</span>  <span class="keywordflow">return</span>(*n1.d_n >= *n2.d_n);</div>
<div class="line"><a name="l00939"></a><span class="lineno"> 939</span>  }</div>
<div class="line"><a name="l00940"></a><span class="lineno"> 940</span> </div>
<div class="line"><a name="l00941"></a><span class="lineno"> 941</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="l00942"></a><span class="lineno"> 942</span>  <span class="keywordflow">return</span>(*n1.d_n != *n2.d_n);</div>
<div class="line"><a name="l00943"></a><span class="lineno"> 943</span>  }</div>
<div class="line"><a name="l00944"></a><span class="lineno"> 944</span> </div>
<div class="line"><a name="l00945"></a><span class="lineno"> 945</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="l00946"></a><span class="lineno"> 946</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n + *n2.d_n));</div>
<div class="line"><a name="l00947"></a><span class="lineno"> 947</span>  }</div>
<div class="line"><a name="l00948"></a><span class="lineno"> 948</span> </div>
<div class="line"><a name="l00949"></a><span class="lineno"> 949</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="l00950"></a><span class="lineno"> 950</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl((*n1.d_n) - (*n2.d_n)));</div>
<div class="line"><a name="l00951"></a><span class="lineno"> 951</span>  }</div>
<div class="line"><a name="l00952"></a><span class="lineno"> 952</span> </div>
<div class="line"><a name="l00953"></a><span class="lineno"> 953</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="l00954"></a><span class="lineno"> 954</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl((*n1.d_n) * (*n2.d_n)));</div>
<div class="line"><a name="l00955"></a><span class="lineno"> 955</span>  }</div>
<div class="line"><a name="l00956"></a><span class="lineno"> 956</span> </div>
<div class="line"><a name="l00957"></a><span class="lineno"> 957</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="l00958"></a><span class="lineno"> 958</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n / *n2.d_n));</div>
<div class="line"><a name="l00959"></a><span class="lineno"> 959</span>  }</div>
<div class="line"><a name="l00960"></a><span class="lineno"> 960</span> </div>
<div class="line"><a name="l00961"></a><span class="lineno"> 961</span>  Unsigned operator%(<span class="keyword">const</span> Unsigned &n1, <span class="keyword">const</span> Unsigned &n2) {</div>
<div class="line"><a name="l00962"></a><span class="lineno"> 962</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n % *n2.d_n));</div>
<div class="line"><a name="l00963"></a><span class="lineno"> 963</span>  }</div>
<div class="line"><a name="l00964"></a><span class="lineno"> 964</span> </div>
<div class="line"><a name="l00965"></a><span class="lineno"> 965</span>  Unsigned <a class="code" href="namespaceCVC3.html#a6b7e38d3c97da1e91e12a6c9555b8163">operator<<</a>(<span class="keyword">const</span> Unsigned& n1, <span class="keywordtype">unsigned</span> n2) {</div>
<div class="line"><a name="l00966"></a><span class="lineno"> 966</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n << n2));</div>
<div class="line"><a name="l00967"></a><span class="lineno"> 967</span>  }</div>
<div class="line"><a name="l00968"></a><span class="lineno"> 968</span> </div>
<div class="line"><a name="l00969"></a><span class="lineno"> 969</span>  Unsigned operator&(<span class="keyword">const</span> Unsigned& n1, <span class="keyword">const</span> Unsigned& n2) {</div>
<div class="line"><a name="l00970"></a><span class="lineno"> 970</span>  <span class="keywordflow">return</span> Unsigned(Unsigned::Impl(*n1.d_n & *n2.d_n));</div>
<div class="line"><a name="l00971"></a><span class="lineno"> 971</span>  }</div>
<div class="line"><a name="l00972"></a><span class="lineno"> 972</span> </div>
<div class="line"><a name="l00973"></a><span class="lineno"> 973</span>  Unsigned Rational::getUnsignedMP()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00974"></a><span class="lineno"> 974</span>  checkInt(*<span class="keyword">this</span>, <span class="stringliteral">"getUnsignedMP()"</span>);</div>
<div class="line"><a name="l00975"></a><span class="lineno"> 975</span>  <span class="keywordtype">long</span> <span class="keywordtype">int</span> res = d_n->getNum();</div>
<div class="line"><a name="l00976"></a><span class="lineno"> 976</span>  <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(res >= 0 && res <= (<span class="keywordtype">long</span> <span class="keywordtype">int</span>)UINT_MAX,</div>
<div class="line"><a name="l00977"></a><span class="lineno"> 977</span>  <span class="stringliteral">"Rational::getUnsignedMP(): arithmetic overflow on "</span> + toString() +</div>
<div class="line"><a name="l00978"></a><span class="lineno"> 978</span>  OVERFLOW_MSG);</div>
<div class="line"><a name="l00979"></a><span class="lineno"> 979</span>  <span class="keywordflow">return</span> Unsigned((<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>)res);</div>
<div class="line"><a name="l00980"></a><span class="lineno"> 980</span>  }</div>
<div class="line"><a name="l00981"></a><span class="lineno"> 981</span> </div>
<div class="line"><a name="l00982"></a><span class="lineno"> 982</span> </div>
<div class="line"><a name="l00983"></a><span class="lineno"> 983</span> } <span class="comment">/* close namespace */</span></div>
<div class="line"><a name="l00984"></a><span class="lineno"> 984</span> </div>
<div class="line"><a name="l00985"></a><span class="lineno"> 985</span> <span class="preprocessor">#endif</span></div>
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