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<div class="headertitle"><div class="title">extended_euclid_algorithm.cpp</div></div>
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<a href="../../d9/d5d/extended__euclid__algorithm_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;algorithm&gt;</span> <span class="comment">// for swap function</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> T2&gt;</div>
<div class="foldopen" id="foldopen00025" data-start="{" data-end="}">
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"><a class="line" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217"> 25</a></span><span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(T *r, T *r0, <span class="keyword">const</span> T2 quotient) {</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> T temp = *r;</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> *r = *r0 - (quotient * temp);</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> *r0 = temp;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span>}</div>
</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T1, <span class="keyword">typename</span> T2&gt;</div>
<div class="foldopen" id="foldopen00042" data-start="{" data-end="}">
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"><a class="line" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25"> 42</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a>(T1 A, T1 B, T1 *GCD, T2 *x, T2 *y) {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (B &gt; A)</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> std::swap(A, B); <span class="comment">// Ensure that A &gt;= B</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> T2 s = 0, s0 = 1;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> T2 t = 1, t0 = 0;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> T1 r = B, r0 = A;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">while</span> (r != 0) {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> T1 quotient = r0 / r;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&amp;r, &amp;r0, quotient);</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&amp;s, &amp;s0, quotient);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a>(&amp;t, &amp;t0, quotient);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> *GCD = r0;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> *x = s0;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> *y = t0;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span>}</div>
</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> T2&gt;</div>
<div class="foldopen" id="foldopen00071" data-start="{" data-end="}">
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d"> 71</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(T A, T B, T *GCD, T2 *x, T2 *y) {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">if</span> (B &gt; A)</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> std::swap(A, B); <span class="comment">// Ensure that A &gt;= B</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">if</span> (B == 0) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> *GCD = A;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> *x = 1;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> *y = 0;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(B, A % B, GCD, x, y);</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> T2 temp = *x;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> *x = *y;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> *y = temp - (A / B) * (*y);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span>}</div>
</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span></div>
<div class="foldopen" id="foldopen00088" data-start="{" data-end="}">
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"><a class="line" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 88</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> uint32_t a, b, <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> int32_t x, y;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> std::cin &gt;&gt; a &gt;&gt; b;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a>(a, b, &amp;<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &amp;x, &amp;y);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> std::cout &lt;&lt; <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; y &lt;&lt; std::endl;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <a class="code hl_function" href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a>(a, b, &amp;<a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a>, &amp;x, &amp;y);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> std::cout &lt;&lt; <a class="code hl_function" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a> &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; y &lt;&lt; std::endl;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span>}</div>
</div>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_a1792ac7c33aaf26b860ab55f5652ab25"><div class="ttname"><a href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#a1792ac7c33aaf26b860ab55f5652ab25">extendedEuclid_1</a></div><div class="ttdeci">void extendedEuclid_1(T1 A, T1 B, T1 *GCD, T2 *x, T2 *y)</div><div class="ttdef"><b>Definition</b> <a href="#l00042">extended_euclid_algorithm.cpp:42</a></div></div>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_abe92d63a0ff9bda7e304df510d5dd217"><div class="ttname"><a href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#abe92d63a0ff9bda7e304df510d5dd217">update_step</a></div><div class="ttdeci">void update_step(T *r, T *r0, const T2 quotient)</div><div class="ttdef"><b>Definition</b> <a href="#l00025">extended_euclid_algorithm.cpp:25</a></div></div>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_acba15ca55b3e7dcb91f3c65d72ba052d"><div class="ttname"><a href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#acba15ca55b3e7dcb91f3c65d72ba052d">extendedEuclid</a></div><div class="ttdeci">void extendedEuclid(T A, T B, T *GCD, T2 *x, T2 *y)</div><div class="ttdef"><b>Definition</b> <a href="#l00071">extended_euclid_algorithm.cpp:71</a></div></div>
<div class="ttc" id="aextended__euclid__algorithm_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d9/d5d/extended__euclid__algorithm_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00088">extended_euclid_algorithm.cpp:88</a></div></div>
<div class="ttc" id="agcd__iterative__euclidean_8cpp_html_ae48807fa2b7000afae599e67f327545e"><div class="ttname"><a href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd</a></div><div class="ttdeci">int gcd(int num1, int num2)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/da0/gcd__iterative__euclidean_8cpp_source.html#l00015">gcd_iterative_euclidean.cpp:15</a></div></div>
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