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<div class="title">sparse_table.cpp File Reference</div> </div>
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<p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/">Sparse Table</a> for <code><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347" title="Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost a...">min()</a></code> function.
<p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <code><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347" title="Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost a...">min()</a></code> function.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
@@ -112,21 +111,21 @@ Include dependency graph for sparse_table.cpp:</div>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">data_structures::sparse_table::Sparse_table</a></td></tr>
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<tr class="memitem:d5/d3c/namespacedata__structures"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d3c/namespacedata__structures.html">data_structures</a></td></tr>
<tr class="memdesc:d5/d3c/namespacedata__structures"><td class="mdescLeft">&#160;</td><td class="mdescRight">Data Structures algorithms. <br /></td></tr>
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<tr class="memdesc:d9/d55/namespacesparse__table"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/">Sparse Table</a> <br /></td></tr>
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<tr class="memdesc:d9/d55/namespacesparse__table"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">More...</a><br /></td></tr>
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Variables</h2></td></tr>
<tr class="memitem:a10f3ffb3f6f7e1b83d556b9c8de89a5d"><td class="memItemLeft" align="right" valign="top">constexpr uint32_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a> = 12345</td></tr>
<tr class="memdesc:a10f3ffb3f6f7e1b83d556b9c8de89a5d"><td class="mdescLeft">&#160;</td><td class="mdescRight">A struct to represent sparse table for <code><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347" title="Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost a...">min()</a></code> as their invariant function, for the given array <code>A</code>. The answer to queries are stored in the array ST. <a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">More...</a><br /></td></tr>
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constexpr uint8_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#af7db62f21983565c64d5d42d2a49888e">data_structures::sparse_table::M</a> = 14</td></tr>
<tr class="memitem:af7db62f21983565c64d5d42d2a49888e"><td class="memItemLeft" align="right" valign="top"><a id="af7db62f21983565c64d5d42d2a49888e" name="af7db62f21983565c64d5d42d2a49888e"></a>
constexpr uint8_t&#160;</td><td class="memItemRight" valign="bottom"><b>data_structures::sparse_table::M</b> = 14</td></tr>
<tr class="memdesc:af7db62f21983565c64d5d42d2a49888e"><td class="mdescLeft">&#160;</td><td class="mdescRight">ceil(log2(N)). <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/">Sparse Table</a> for <code><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347" title="Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost a...">min()</a></code> function. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/manncodes">Mann Patel</a></dd></dl>
<div class="textblock"><p >Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <code><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347" title="Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost a...">min()</a></code> function. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/manncodes" target="_blank">Mann Patel</a></dd></dl>
<p>Sparse Table is a data structure, that allows answering range queries. It can answer most range queries in O(logn), but its true power is answering range minimum queries (or equivalent range maximum queries). For those queries it can compute the answer in O(1) time. The only drawback of this data structure is, that it can only be used on immutable arrays. This means, that the array cannot be changed between two queries.</p>
<p>If any element in the array changes, the complete data structure has to be recomputed.</p>
<p >If any element in the array changes, the complete data structure has to be recomputed.</p>
<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000004">Todo:</a></b></dt><dd>make stress tests.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>This sparse table is made for <code>min(a1,a2,...an)</code> duplicate invariant function. This implementation can be changed to other functions like <code><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd()</a></code>, <code><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a></code>, and <code>max()</code> by changing a few lines of code. </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; {</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> {</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_function" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span>}</div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:128</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>&lt; array on which RMQ will be performed.</p>
<p>&lt; size of self test's array</p>
<p>&lt; declaring sparse tree</p>
<p>&lt; copying array to the struct</p>
<p>&lt; passing the array's size to the struct</p>
<p>&lt; precomputing sparse tree</p>
<p>&lt; as 1 is smallest from 1..9</p>
<p>&lt; as 2 is smallest from 2..6</p>
<p>&lt; as 3 is smallest from 3..8</p>
<div class="fragment"><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="comment">/* We take an array as an input on which we need to perform the ranged</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;<span class="comment"> * minimum queries[RMQ](https://en.wikipedia.org/wiki/Range_minimum_query).</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int64_t, 10&gt;</a> testcase = {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; 1, 2, 3, 4, 5,</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; 6, 7, 8, 9, 10}; <span class="comment">///&lt; array on which RMQ will be performed.</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="keywordtype">size_t</span> testcase_size =</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; <span class="keyword">sizeof</span>(testcase) / <span class="keyword">sizeof</span>(testcase[0]); <span class="comment">///&lt; size of self test&#39;s array</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; <a class="code" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">data_structures::sparse_table::Sparse_table</a></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; st{}; <span class="comment">///&lt; declaring sparse tree</span></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; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/copy.html">std::copy</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(testcase), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(testcase),</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(st.A)); <span class="comment">///&lt; copying array to the struct</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; st.n = testcase_size; <span class="comment">///&lt; passing the array&#39;s size to the struct</span></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; st.buildST(); <span class="comment">///&lt; precomputing sparse tree</span></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="comment">// pass queries of the form: [l,r]</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; assert(st.query(1, 9) == 1); <span class="comment">///&lt; as 1 is smallest from 1..9</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; assert(st.query(2, 6) == 2); <span class="comment">///&lt; as 2 is smallest from 2..6</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; assert(st.query(3, 8) == 3); <span class="comment">///&lt; as 3 is smallest from 3..8</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160; </div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</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;Self-test implementations passed!&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="l00153"></a><span class="lineno"> 153</span>&#160;}</div>
<p >&lt; array on which RMQ will be performed.</p>
<p >&lt; size of self test's array</p>
<p >&lt; declaring sparse tree</p>
<p >&lt; copying array to the struct</p>
<p >&lt; passing the array's size to the struct</p>
<p >&lt; precomputing sparse tree</p>
<p >&lt; as 1 is smallest from 1..9</p>
<p >&lt; as 2 is smallest from 2..6</p>
<p >&lt; as 3 is smallest from 3..8</p>
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<p>A struct to represent sparse table for <code><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347" title="Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost a...">min()</a></code> as their invariant function, for the given array <code>A</code>. The answer to queries are stored in the array ST. </p>
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<p >the maximum size of the array. </p>
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<a href="#func-members">Functions</a> </div>
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<div class="title">miller_rabin.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">miller_rabin.cpp File Reference</div></div>
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<div class="contents">
<div class="textblock"><code>#include &lt;cassert&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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<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>
<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>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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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>
<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> {</div>
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Here is the call graph for this function:</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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<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>
<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>
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<tr><td class="paramname">repeats</td><td>number of repetitions for the test to increase probability of correct result. </td></tr>
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<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>
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<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>
<div class="fragment"><div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">if</span> (num &lt;= 4) {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// If num == 2 or num == 3 then prime</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">if</span> (num == 2 || num == 3) {</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> }</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// If num is even then not prime</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordflow">if</span> (num % 2 == 0) {</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> }</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// Finding d and r in num = 2^r * d + 1</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> T d = num - 1, r = 0;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">while</span> (d % 2 == 0) {</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> d = d / 2;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> r++;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> }</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> </div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keywordflow">for</span> (T i = 0; i &lt; repeats; ++i) {</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a>(d, num)) {</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> }</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> }</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span>}</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>
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@@ -235,7 +234,7 @@ Here is the call graph for this function:</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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@@ -262,7 +261,7 @@ template&lt;typename T &gt; </div>
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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>
<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>
@@ -272,39 +271,39 @@ 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="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="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">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, power, 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>
<div class="fragment"><div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// random number seed</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <a class="code hl_classRef" 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 id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// random number generator</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_classRef" 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 id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// Uniformly distributed range [2, num - 2] for random numbers</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_classRef" 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 id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// Random number generated in the range [2, num -2].</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> T random = distribution(gen);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// vector for reverse binary of the power</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a> = <a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#a091662a787d5ad4866713021f580fddb">reverse_binary</a>(d);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// x = random ^ d % num</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> T x = <a class="code hl_function" href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a>(random, power, num);</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// miller conditions</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">if</span> (x == 1 || x == num - 1) {</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">while</span> (d != num - 1) {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> x = (x * x) % num;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> d *= 2;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span> (x == 1) {</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> }</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">if</span> (x == num - 1) {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_a7cf5feaf168b88e74544da59ed830311"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">math::fibonacci_sum::power</a></div><div class="ttdeci">math::fibonacci_sum::matrix power(math::fibonacci_sum::matrix T, uint64_t ex)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:57</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="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="amiller__rabin_8cpp_html_a091662a787d5ad4866713021f580fddb"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a091662a787d5ad4866713021f580fddb">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="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="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="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>
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<a id="ad6c2c67ea416d0e80003a88623f98b29"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ad6c2c67ea416d0e80003a88623f98b29">&#9670;&nbsp;</a></span>modular_exponentiation()</h2>
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</tr>
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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>
<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>
@@ -360,25 +359,25 @@ 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="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>
<div class="fragment"><div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">if</span> (mod == 1)</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> T b = 1;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">if</span> (rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 0)</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">return</span> b;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> T A = base;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">if</span> (rev_binary_exponent[0] == 1)</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> b = base;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="code hl_classRef" 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 id="l00055" name="l00055"></a><span class="lineno"> 55</span> rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">cbegin</a>() + 1;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> it != rev_binary_exponent.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">cend</a>(); ++it) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> A = A * A % mod;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">if</span> (*it == 1)</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">return</span> b;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span>}</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>
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<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>
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<h2 class="memtitle"><span class="permalink"><a href="#a798398d5bfd375a3c0ce68100842f6f5">&#9670;&nbsp;</a></span>reverse_binary()</h2>
<a id="a091662a787d5ad4866713021f580fddb" name="a091662a787d5ad4866713021f580fddb"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a091662a787d5ad4866713021f580fddb">&#9670;&nbsp;</a></span>reverse_binary()</h2>
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@@ -400,7 +399,7 @@ Here is the call graph for this function:</div>
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<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 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>
@@ -408,27 +407,27 @@ template&lt;typename T &gt; </div>
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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>
<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> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</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; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(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> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> {</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> T temp = num;</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keywordflow">while</span> (temp &gt; 0) {</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.push_back(temp % 2);</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> temp = temp / 2;</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> }</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span>}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&nbsp;</a></span>tests()</h2>
<div class="memitem">
@@ -442,29 +441,29 @@ template&lt;typename T &gt; </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="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>
<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 id="l00157" name="l00157"></a><span class="lineno"> 157</span> {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// First test on 2</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> 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 id="l00160" name="l00160"></a><span class="lineno"> 160</span> <a class="code hl_function" 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 id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="comment">// Second test on 5</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> 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 id="l00164" name="l00164"></a><span class="lineno"> 164</span> <a class="code hl_function" 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 id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// Third test on 23</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> 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 id="l00168" name="l00168"></a><span class="lineno"> 168</span> <a class="code hl_function" 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 id="l00169" name="l00169"></a><span class="lineno"> 169</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// Fourth test on 16</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> 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 id="l00172" name="l00172"></a><span class="lineno"> 172</span> <a class="code hl_function" 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 id="l00173" name="l00173"></a><span class="lineno"> 173</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// Fifth test on 27</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> 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 id="l00176" name="l00176"></a><span class="lineno"> 176</span> <a class="code hl_function" 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 id="l00177" name="l00177"></a><span class="lineno"> 177</span> <a class="code hl_classRef" 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="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span>}</div>
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