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@@ -145,10 +145,10 @@ Functions</h2></td></tr>
</table>
</div><div class="memdoc">
<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; {</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; <a class="code" href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;}</div>
<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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@@ -196,33 +196,33 @@ template&lt;typename T &gt; </div>
<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="l00122"></a><span class="lineno"> 122</span>&#160; {</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <span class="keywordflow">if</span> (num &lt;= 4) {</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; <span class="comment">// If num == 2 or num == 3 then prime</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <span class="keywordflow">if</span> (num == 2 || num == 3) {</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; }</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; }</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; <span class="comment">// If num is even then not prime</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <span class="keywordflow">if</span> (num % 2 == 0) {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; }</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="comment">// Finding d and r in num = 2^r * d + 1</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; T d = num - 1, r = 0;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; <span class="keywordflow">while</span> (d % 2 == 0) {</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; d = d / 2;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; r++;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; }</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; </div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; <span class="keywordflow">for</span> (T i = 0; i &lt; repeats; ++i) {</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</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="l00144"></a><span class="lineno"> 144</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; }</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;}</div>
<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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@@ -269,36 +269,36 @@ template&lt;typename T &gt; </div>
<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="l00071"></a><span class="lineno"> 71</span>&#160; {</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// random number seed</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</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="l00074"></a><span class="lineno"> 74</span>&#160; <span class="comment">// random number generator</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/mersenne_twister_engine.html">std::mt19937</a> gen(rd_seed());</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="comment">// Uniformly distributed range [2, num - 2] for random numbers</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/uniform_int_distribution.html">std::uniform_int_distribution&lt;&gt;</a> distribution(2, num - 2);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// Random number generated in the range [2, num -2].</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; T random = distribution(gen);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// vector for reverse binary of the power</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</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="l00082"></a><span class="lineno"> 82</span>&#160; <span class="comment">// x = random ^ d % num</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</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="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// miller conditions</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordflow">if</span> (x == 1 || x == num - 1) {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keywordflow">while</span> (d != num - 1) {</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; x = (x * x) % num;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; d *= 2;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="keywordflow">if</span> (x == 1) {</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">if</span> (x == num - 1) {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; }</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; }</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;}</div>
<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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@@ -350,25 +350,25 @@ template&lt;typename T &gt; </div>
</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="l00043"></a><span class="lineno"> 43</span>&#160; {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">if</span> (mod == 1)</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; T b = 1;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</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="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">return</span> b;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; T A = base;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">if</span> (rev_binary_exponent[0] == 1)</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; b = base;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</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="l00054"></a><span class="lineno"> 54</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="l00055"></a><span class="lineno"> 55</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="l00056"></a><span class="lineno"> 56</span>&#160; A = A * A % mod;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">if</span> (*it == 1)</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; b = A * b % mod;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; }</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">return</span> b;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160;}</div>
<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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@@ -396,15 +396,15 @@ template&lt;typename T &gt; </div>
</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="l00018"></a><span class="lineno"> 18</span>&#160; {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</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="l00020"></a><span class="lineno"> 20</span>&#160; T temp = num;</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; <span class="keywordflow">while</span> (temp &gt; 0) {</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</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="l00023"></a><span class="lineno"> 23</span>&#160; temp = temp / 2;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; }</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;}</div>
<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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@@ -429,28 +429,28 @@ Here is the call graph for this function:</div>
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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="l00154"></a><span class="lineno"> 154</span>&#160; {</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; <span class="comment">// First test on 2</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</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="l00157"></a><span class="lineno"> 157</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="l00158"></a><span class="lineno"> 158</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="l00159"></a><span class="lineno"> 159</span>&#160; <span class="comment">// Second test on 5</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</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="l00161"></a><span class="lineno"> 161</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="l00162"></a><span class="lineno"> 162</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="l00163"></a><span class="lineno"> 163</span>&#160; <span class="comment">// Third test on 23</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</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="l00165"></a><span class="lineno"> 165</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="l00166"></a><span class="lineno"> 166</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="l00167"></a><span class="lineno"> 167</span>&#160; <span class="comment">// Fourth test on 16</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</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="l00169"></a><span class="lineno"> 169</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="l00170"></a><span class="lineno"> 170</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="l00171"></a><span class="lineno"> 171</span>&#160; <span class="comment">// Fifth test on 27</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</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="l00173"></a><span class="lineno"> 173</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="l00174"></a><span class="lineno"> 174</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="l00175"></a><span class="lineno"> 175</span>&#160;}</div>
<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><!-- doc-content -->
<div class="ttc" id="auniform_int_distribution_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution</a></div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a901288288ef5ebe8e97414cc30797cce"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a></div><div class="ttdeci">bool miller_rabin_primality_test(T num, T repeats)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:122</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a901288288ef5ebe8e97414cc30797cce"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a></div><div class="ttdeci">bool miller_rabin_primality_test(T num, T repeats)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:125</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a798398d5bfd375a3c0ce68100842f6f5"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a></div><div class="ttdeci">std::vector&lt; T &gt; reverse_binary(T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:18</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a798398d5bfd375a3c0ce68100842f6f5"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a></div><div class="ttdeci">std::vector&lt; T &gt; reverse_binary(T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:19</div></div>
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_ae249a2af508aa94266023ce8aa81426f"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a></div><div class="ttdeci">void power(int x, int n)</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:56</div></div>
<div class="ttc" id="amersenne_twister_engine_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a></div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="arandom_device_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a></div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<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:42</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a6f9c31c1047aa3191676d64571d4c506"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a></div><div class="ttdeci">bool miller_test(T d, T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:71</div></div>
<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>
<div class="ttc" id="amiller__rabin_8cpp_html_a6f9c31c1047aa3191676d64571d4c506"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a></div><div class="ttdeci">bool miller_test(T d, T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:73</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::cbegin</a></div><div class="ttdeci">T cbegin(T... args)</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::cend</a></div><div class="ttdeci">T cend(T... args)</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:154</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:157</div></div>
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