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<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;random&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Functions</h2></td></tr>
<tr class="memitem:a798398d5bfd375a3c0ce68100842f6f5"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a798398d5bfd375a3c0ce68100842f6f5"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a> (T num)</td></tr>
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<tr class="memitem:ad6c2c67ea416d0e80003a88623f98b29"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a> (T base, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;rev_binary_exponent, T mod)</td></tr>
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<tr class="memitem:a6f9c31c1047aa3191676d64571d4c506"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a> (T d, T num)</td></tr>
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<tr class="memitem:a901288288ef5ebe8e97414cc30797cce"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a> (T num, T repeats)</td></tr>
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<tr class="memitem:a88ec9ad42717780d6caaff9d3d6977f9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>tjgurwara99</dd></dl>
<p>A basic implementation of Miller-Rabin primality test. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; {</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a901288288ef5ebe8e97414cc30797cce">&#9670;&nbsp;</a></span>miller_rabin_primality_test()</h2>
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<td class="memname">bool miller_rabin_primality_test </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>num</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>repeats</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Function that test (probabilistically) whether a given number is a prime based on the Miller-Rabin Primality Test. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">num</td><td>number to be tested for primality. </td></tr>
<tr><td class="paramname">repeats</td><td>number of repetitions for the test to increase probability of correct result. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>'false' if num is composite </dd>
<dd>
'true' if num is (probably) prime</dd></dl>
<p>\detail First we check whether the num input is less than 4, if so we can determine whether this is a prime or composite by checking for 2 and 3. Next we check whether this num is odd (as all primes greater than 2 are odd). Next we write our num in the following format \(num = 2^r \cdot d + 1\). After finding r and d for our input num, we use for loop repeat number of times inside which we check the miller conditions using the function miller_test. If miller_test returns false then the number is composite After the loop finishes completely without issuing a false return call, we can conclude that this number is probably prime. </p>
<div class="fragment"><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; {</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordflow">if</span> (num &lt;= 4) {</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="comment">// If num == 2 or num == 3 then prime</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">if</span> (num == 2 || num == 3) {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; }</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; }</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <span class="comment">// If num is even then not prime</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="keywordflow">if</span> (num % 2 == 0) {</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; }</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; <span class="comment">// Finding d and r in num = 2^r * d + 1</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; T d = num - 1, r = 0;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; <span class="keywordflow">while</span> (d % 2 == 0) {</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; d = d / 2;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; r++;</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; <span class="keywordflow">for</span> (T i = 0; i &lt; repeats; ++i) {</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a>(d, num)) {</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; }</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; }</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6f9c31c1047aa3191676d64571d4c506">&#9670;&nbsp;</a></span>miller_test()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">bool miller_test </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>d</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>num</em>&#160;</td>
</tr>
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<p>Function for testing the conditions that are satisfied when a number is prime. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">d</td><td>number such that \(d \cdot 2^r = n - 1\) where \(n = num\) parameter and \(r \geq 1\) </td></tr>
<tr><td class="paramname">num</td><td>number being tested for primality. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>'false' if n is composite </dd>
<dd>
'true' if n is (probably) prime. </dd></dl>
<div class="fragment"><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="comment">// random number seed</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a> rd_seed;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="comment">// random number generator</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a> gen(rd_seed());</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// Uniformly distributed range [2, num - 2] for random numbers</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution&lt;&gt;</a> distribution(2, num - 2);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// Random number generated in the range [2, num -2].</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; T random = distribution(gen);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="comment">// vector for reverse binary of the power</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> = <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a>(d);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// x = random ^ d % num</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; T x = <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a>(random, <a class="code" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>, num);</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="comment">// miller conditions</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="keywordflow">if</span> (x == 1 || x == num - 1) {</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; }</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keywordflow">while</span> (d != num - 1) {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; x = (x * x) % num;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; d *= 2;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">if</span> (x == 1) {</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; }</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordflow">if</span> (x == num - 1) {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; }</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ad6c2c67ea416d0e80003a88623f98b29">&#9670;&nbsp;</a></span>modular_exponentiation()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">T modular_exponentiation </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>base</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>rev_binary_exponent</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>mod</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>Function for modular exponentiation. This function is an efficient modular exponentiation function. It can be used with any big integer library such as Boost multiprecision to give result any modular exponentiation problem relatively quickly. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">base</td><td>number being raised to a power as integer </td></tr>
<tr><td class="paramname">rev_binary_exponent</td><td>reverse binary of the power the base is being raised to </td></tr>
<tr><td class="paramname">mod</td><td>modulo </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>r the modular exponentiation of \(a^{n} \equiv r \mod{m}\) where \(n\) is the base 10 representation of rev_binary_exponent and \(m = mod \) parameter. </dd></dl>
<div class="fragment"><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">if</span> (mod == 1)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; T b = 1;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">if</span> (rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0)</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">return</span> b;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; T A = base;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">if</span> (rev_binary_exponent[0] == 1)</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; b = base;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;::const_iterator</a> it =</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">cbegin</a>() + 1;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; it != rev_binary_exponent.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">cend</a>(); ++it) {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; A = A * A % mod;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">if</span> (*it == 1)</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; b = A * b % mod;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">return</span> b;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a798398d5bfd375a3c0ce68100842f6f5">&#9670;&nbsp;</a></span>reverse_binary()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; reverse_binary </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>num</em></td><td>)</td>
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<p>Function to give a binary representation of a number in reverse order </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">num</td><td>integer number that we want to convert </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>result vector of the number input in reverse binary </dd></dl>
<div class="fragment"><div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160; {</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> result;</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; T temp = num;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keywordflow">while</span> (temp &gt; 0) {</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; result.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(temp % 2);</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; temp = temp / 2;</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; }</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&nbsp;</a></span>tests()</h2>
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<td class="memname">void tests </td>
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<p>Functions for testing the <a class="el" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test()</a> function with some assert statements. </p>
<div class="fragment"><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; <span class="comment">// First test on 2</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;2 is prime but function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(2, 1) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;First test passes.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; <span class="comment">// Second test on 5</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;5 should be prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(5, 3) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Second test passes.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <span class="comment">// Third test on 23</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;23 should be prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(23, 3) == <span class="keyword">true</span>));</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Third test passes.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; <span class="comment">// Fourth test on 16</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;16 is not a prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(16, 3) == <span class="keyword">false</span>));</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Fourth test passes.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; <span class="comment">// Fifth test on 27</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;27 is not a prime but the function says otherwise.\n&quot;</span>,</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a>(27, 3) == <span class="keyword">false</span>));</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Fifth test passes.&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160;}</div>
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<div class="ttc" id="amiller__rabin_8cpp_html_ad6c2c67ea416d0e80003a88623f98b29"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a></div><div class="ttdeci">T modular_exponentiation(T base, const std::vector&lt; T &gt; &amp;rev_binary_exponent, T mod)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:43</div></div>
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