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@@ -297,6 +297,7 @@ Math</h1>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_of_n_numbers.cpp">Gcd Of N Numbers</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_recursive_euclidean.cpp">Gcd Recursive Euclidean</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/integral_approximation.cpp">Integral Approximation</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/inv_sqrt.cpp">Inv Sqrt</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_factorial.cpp">Large Factorial</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_number.h">Large Number</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/largest_power.cpp">Largest Power</a></li>
@@ -469,7 +470,7 @@ Strings</h1>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/brute_force_string_searching.cpp">Brute Force String Searching</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/horspool.cpp">Horspool</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/knuth_morris_pratt.cpp">Knuth Morris Pratt</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/manacher_algorithm.cpp">Manacher's Algorithm</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/manacher_algorithm.cpp">Manacher Algorithm</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/rabin_karp.cpp">Rabin Karp</a> </li>
</ul>
</div></div><!-- contents -->

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<p>Implementation of <a href="https://medium.com/hard-mode/the-legendary-fast-inverse-square-root-e51fee3b49d9">the inverse square root Root</a>.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;limits&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for inv_sqrt.cpp:</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ad219034bf5fba657f5035ec5a1d50f52"><td class="memTemplParams" colspan="2">template&lt;typename T = double, char iterations = 2&gt; </td></tr>
<tr class="memitem:ad219034bf5fba657f5035ec5a1d50f52"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a> (T x)</td></tr>
<tr class="memdesc:ad219034bf5fba657f5035ec5a1d50f52"><td class="mdescLeft">&#160;</td><td class="mdescRight">for numeric_limits <a href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">More...</a><br /></td></tr>
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<tr class="memitem:aa2703e5cf3fecde8becd9066b9666b97"><td class="memTemplParams" colspan="2">template&lt;typename T = double&gt; </td></tr>
<tr class="memitem:aa2703e5cf3fecde8becd9066b9666b97"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a> (T number)</td></tr>
<tr class="memdesc:aa2703e5cf3fecde8becd9066b9666b97"><td class="mdescLeft">&#160;</td><td class="mdescRight">This is the function that calculates the fast inverse square root. The following code is the fast inverse square root with standard lib (cmath) More information can be found at <a href="https://www.linkedin.com/pulse/fast-inverse-square-root-still-armin-kassemi-langroodi">LinkedIn</a> <a href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">More...</a><br /></td></tr>
<tr class="separator:aa2703e5cf3fecde8becd9066b9666b97"><td class="memSeparator" colspan="2">&#160;</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/db8/inv__sqrt_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/db8/inv__sqrt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/db8/inv__sqrt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d6/db8/inv__sqrt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><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://medium.com/hard-mode/the-legendary-fast-inverse-square-root-e51fee3b49d9">the inverse square root Root</a>. </p>
<p>Two implementation to calculate inverse inverse root, from Quake III Arena (C++ version) and with a standard library (<code>cmath</code>). This algorithm is used to calculate shadows in Quake III Arena. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ad219034bf5fba657f5035ec5a1d50f52"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad219034bf5fba657f5035ec5a1d50f52">&#9670;&nbsp;</a></span>Fast_InvSqrt()</h2>
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template&lt;typename T = double, char iterations = 2&gt; </div>
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<td class="memname">T Fast_InvSqrt </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
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<span class="mlabels"><span class="mlabel">inline</span></span> </td>
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</div><div class="memdoc">
<p>for numeric_limits </p>
<p>for assert for <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></code> for IO operations</p>
<p>This is the function that calculates the fast inverse square root. The following code is the fast inverse square root implementation from Quake III Arena (Adapted for C++). More information can be found at <a href="https://en.wikipedia.org/wiki/Fast_inverse_square_root">Wikipedia</a> </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>floating type </td></tr>
<tr><td class="paramname">iterations</td><td>inverse square root, the greater the number of iterations, the more exact the result will be (1 or 2). </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>value to calculate </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the inverse square root </dd></dl>
<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keyword">using</span> Tint = <span class="keyword">typename</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/conditional.html">std::conditional</a>&lt;<span class="keyword">sizeof</span>(T) == 8, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int64_t</a>,</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int32_t</a>&gt;::type;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; T y = x;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; T x2 = y * 0.5;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; Tint i =</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; *<span class="keyword">reinterpret_cast&lt;</span>Tint *<span class="keyword">&gt;</span>(&amp;y); <span class="comment">// Store floating-point bits in integer</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; i = (<span class="keyword">sizeof</span>(T) == 8 ? 0x5fe6eb50c7b537a9 : 0x5f3759df) -</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; (i &gt;&gt; 1); <span class="comment">// Initial guess for Newton&#39;s method</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; y = *<span class="keyword">reinterpret_cast&lt;</span>T *<span class="keyword">&gt;</span>(&amp;i); <span class="comment">// Convert new bits into float</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; y = y * (1.5 - (x2 * y * y)); <span class="comment">// 1st iteration Newton&#39;s method</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">if</span> (iterations == 2) {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; y = y * (1.5 - (x2 * y * y)); <span class="comment">// 2nd iteration, the more exact result</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">return</span> y;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;}</div>
<div class="ttc" id="aconditional_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/conditional.html">std::conditional</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><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; <a class="code" href="../../d6/db8/inv__sqrt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</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;The Fast inverse square root of 36 is: &quot;</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; &lt;&lt; Fast_InvSqrt&lt;float, 1&gt;(36.0f) &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="l00091"></a><span class="lineno"> 91</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;The Fast inverse square root of 36 is: &quot;</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; &lt;&lt; Fast_InvSqrt&lt;double, 2&gt;(36.0f) &lt;&lt; <span class="stringliteral">&quot; (2 iterations)&quot;</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; &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="l00094"></a><span class="lineno"> 94</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;The Fast inverse square root of 100 is: &quot;</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; &lt;&lt; <a class="code" href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a>(100.0f)</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; &lt;&lt; <span class="stringliteral">&quot; (With default template type and iterations: double, 2)&quot;</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; &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="l00098"></a><span class="lineno"> 98</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;The Standard inverse square root of 36 is: &quot;</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; &lt;&lt; Standard_InvSqrt&lt;float&gt;(36.0f) &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="l00100"></a><span class="lineno"> 100</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;The Standard inverse square root of 100 is: &quot;</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; &lt;&lt; <a class="code" href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a>(100.0f)</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; &lt;&lt; <span class="stringliteral">&quot; (With default template type: double)&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="l00103"></a><span class="lineno"> 103</span>&#160;}</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="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="ainv__sqrt_8cpp_html_aa2703e5cf3fecde8becd9066b9666b97"><div class="ttname"><a href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a></div><div class="ttdeci">T Standard_InvSqrt(T number)</div><div class="ttdoc">This is the function that calculates the fast inverse square root. The following code is the fast inv...</div><div class="ttdef"><b>Definition:</b> inv_sqrt.cpp:59</div></div>
<div class="ttc" id="ainv__sqrt_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d6/db8/inv__sqrt_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> inv_sqrt.cpp:68</div></div>
<div class="ttc" id="ainv__sqrt_8cpp_html_ad219034bf5fba657f5035ec5a1d50f52"><div class="ttname"><a href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a></div><div class="ttdeci">T Fast_InvSqrt(T x)</div><div class="ttdoc">for numeric_limits</div><div class="ttdef"><b>Definition:</b> inv_sqrt.cpp:28</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa2703e5cf3fecde8becd9066b9666b97">&#9670;&nbsp;</a></span>Standard_InvSqrt()</h2>
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template&lt;typename T = double&gt; </div>
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<td class="memname">T Standard_InvSqrt </td>
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<p>This is the function that calculates the fast inverse square root. The following code is the fast inverse square root with standard lib (cmath) More information can be found at <a href="https://www.linkedin.com/pulse/fast-inverse-square-root-still-armin-kassemi-langroodi">LinkedIn</a> </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">number</td><td>value to calculate </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the inverse square root </dd></dl>
<div class="fragment"><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; T squareRoot = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">sqrt</a>(number);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">return</span> 1.0f / squareRoot;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;}</div>
<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</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>
<div class="fragment"><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keyword">const</span> <span class="keywordtype">float</span> epsilon = 1e-3f;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="comment">/* Tests with multiple values */</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;float&gt;(100.0f) - 0.0998449f) &lt; epsilon);</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;double&gt;(36.0f) - 0.166667f) &lt; epsilon);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(<a class="code" href="../../d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">Standard_InvSqrt</a>(12.0f) - 0.288423f) &lt; epsilon);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Standard_InvSqrt&lt;double&gt;(5.0f) - 0.447141f) &lt; epsilon);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;float, 1&gt;(100.0f) - 0.0998449f) &lt; epsilon);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;double, 1&gt;(36.0f) - 0.166667f) &lt; epsilon);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(<a class="code" href="../../d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">Fast_InvSqrt</a>(12.0f) - 0.288423) &lt; epsilon);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/fabs.html">std::fabs</a>(Fast_InvSqrt&lt;double&gt;(5.0f) - 0.447141) &lt; epsilon);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;}</div>
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<tr id="row_13_27_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d44/magic__number_8cpp.html" target="_self">magic_number.cpp</a></td><td class="desc">A simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number </td></tr>
<tr id="row_13_28_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d42/miller__rabin_8cpp.html" target="_self">miller_rabin.cpp</a></td><td class="desc"></td></tr>
<tr id="row_13_29_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d72/modular__division_8cpp.html" target="_self">modular_division.cpp</a></td><td class="desc">An algorithm to divide two numbers under modulo p <a href="https://www.geeksforgeeks.org/modular-division">Modular Division</a> </td></tr>
<tr id="row_13_30_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d6d/modular__exponentiation_8cpp.html" target="_self">modular_exponentiation.cpp</a></td><td class="desc">C++ Program for Modular Exponentiation Iteratively </td></tr>
<tr id="row_13_31_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html" target="_self">modular_inverse_fermat_little_theorem.cpp</a></td><td class="desc">C++ Program to find the modular inverse using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem">Fermat's Little Theorem</a> </td></tr>
<tr id="row_13_32_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d27/n__bonacci_8cpp.html" target="_self">n_bonacci.cpp</a></td><td class="desc">Implementation of the <a href="http://oeis.org/wiki/N-bonacci_numbers">N-bonacci</a> series </td></tr>
<tr id="row_13_33_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/dbb/n__choose__r_8cpp.html" target="_self">n_choose_r.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Combination">Combinations</a> n choose r function implementation </td></tr>
<tr id="row_13_34_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/dab/ncr__modulo__p_8cpp.html" target="_self">ncr_modulo_p.cpp</a></td><td class="desc">This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html">nCr modulo p</a> </td></tr>
<tr id="row_13_35_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html" target="_self">number_of_positive_divisors.cpp</a></td><td class="desc">C++ Program to calculate the number of positive divisors </td></tr>
<tr id="row_13_36_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/def/power__for__huge__numbers_8cpp.html" target="_self">power_for_huge_numbers.cpp</a></td><td class="desc">Compute powers of large numbers </td></tr>
<tr id="row_13_37_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d38/power__of__two_8cpp.html" target="_self">power_of_two.cpp</a></td><td class="desc">Implementation to check whether a number is a power of 2 or not </td></tr>
<tr id="row_13_38_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d0d/prime__factorization_8cpp.html" target="_self">prime_factorization.cpp</a></td><td class="desc">Prime factorization of positive integers </td></tr>
<tr id="row_13_39_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d9b/prime__numbers_8cpp.html" target="_self">prime_numbers.cpp</a></td><td class="desc">Get list of prime numbers </td></tr>
<tr id="row_13_40_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html" target="_self">primes_up_to_billion.cpp</a></td><td class="desc">Compute prime numbers upto 1 billion </td></tr>
<tr id="row_13_41_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d08/realtime__stats_8cpp.html" target="_self">realtime_stats.cpp</a></td><td class="desc">Compute statistics for data entered in rreal-time </td></tr>
<tr id="row_13_42_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html" target="_self">sieve_of_eratosthenes.cpp</a></td><td class="desc">Get list of prime numbers using Sieve of Eratosthenes </td></tr>
<tr id="row_13_43_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="da/d24/sqrt__double_8cpp.html" target="_self">sqrt_double.cpp</a></td><td class="desc">Calculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> of root-finding </td></tr>
<tr id="row_13_44_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d47/string__fibonacci_8cpp.html" target="_self">string_fibonacci.cpp</a></td><td class="desc">This Programme returns the Nth fibonacci as a string </td></tr>
<tr id="row_13_45_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9d/sum__of__binomial__coefficient_8cpp.html" target="_self">sum_of_binomial_coefficient.cpp</a></td><td class="desc">Algorithm to find sum of binomial coefficients of a given positive integer </td></tr>
<tr id="row_13_46_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d83/sum__of__digits_8cpp.html" target="_self">sum_of_digits.cpp</a></td><td class="desc">A C++ Program to find the Sum of Digits of input integer </td></tr>
<tr id="row_13_47_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d66/vector__cross__product_8cpp.html" target="_self">vector_cross_product.cpp</a></td><td class="desc">Calculates the <a href="https://en.wikipedia.org/wiki/Cross_product">Cross Product</a> and the magnitude of two mathematical 3D vectors </td></tr>
<tr id="row_14_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_14_" class="arrow" onclick="toggleFolder('14_')">&#9658;</span><span id="img_14_" class="iconfclosed" onclick="toggleFolder('14_')">&#160;</span><a class="el" href="dir_9c6faab82c22511b50177aa2e38e2780.html" target="_self">numerical_methods</a></td><td class="desc"></td></tr>
<tr id="row_14_0_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d7/d6a/bisection__method_8cpp.html" target="_self">bisection_method.cpp</a></td><td class="desc">Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Bisection_method">bisection method</a> </td></tr>
<tr id="row_14_1_" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d01/brent__method__extrema_8cpp.html" target="_self">brent_method_extrema.cpp</a></td><td class="desc">Find real extrema of a univariate real function in a given interval using <a href="https://en.wikipedia.org/wiki/Brent%27s_method">Brent's method</a> </td></tr>

3
globals_f.html
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<li>factors
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">prime_factorization.cpp</a>
</li>
<li>Fast_InvSqrt()
: <a class="el" href="d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">inv_sqrt.cpp</a>
</li>
<li>fast_power_linear()
: <a class="el" href="d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power.cpp</a>
</li>

3
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: <a class="el" href="d9/d00/factorial_8cpp.html#ae9945c15826a9c1b5c141db314b7f8b4">factorial.cpp</a>
</li>
<li>Fast_InvSqrt()
: <a class="el" href="d6/db8/inv__sqrt_8cpp.html#ad219034bf5fba657f5035ec5a1d50f52">inv_sqrt.cpp</a>
</li>
<li>fast_power_linear()
: <a class="el" href="d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power.cpp</a>
</li>

1
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, <a class="el" href="d4/d45/gcd__recursive__euclidean_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">gcd_recursive_euclidean.cpp</a>
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, <a class="el" href="d5/d7a/largest__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">largest_power.cpp</a>
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9
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<li>show_pascal()
: <a class="el" href="dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">pascal_triangle.cpp</a>
</li>
<li>sieve()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a60fa6579eab0db3c1c0ab1bf6d651be3">sieve_of_eratosthenes.cpp</a>
</li>
<li>Sieve()
: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a>
</li>
<li>sieve()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a60fa6579eab0db3c1c0ab1bf6d651be3">sieve_of_eratosthenes.cpp</a>
</li>
<li>SieveOfEratosthenes()
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">prime_factorization.cpp</a>
</li>
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<li>Sqrt()
: <a class="el" href="da/d24/sqrt__double_8cpp.html#ae662282ad0740d2063ac404ca3bd74fc">sqrt_double.cpp</a>
</li>
<li>Standard_InvSqrt()
: <a class="el" href="d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">inv_sqrt.cpp</a>
</li>
<li>struzik_search()
: <a class="el" href="d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">exponential_search.cpp</a>
</li>

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1
globals_m.html
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, <a class="el" href="d5/d7a/largest__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">largest_power.cpp</a>
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globals_p.html
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@@ -130,12 +130,12 @@ $(document).ready(function(){initNavTree('globals_p.html',''); initResizable();
<li>predict_OLS_regressor()
: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">ordinary_least_squares_regressor.cpp</a>
</li>
<li>PRIME
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</li>
<li>prime
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</li>
<li>PRIME
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</li>
<li>prime_factorization()
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization.cpp</a>
</li>

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<li>show_pascal()
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</li>
<li>sieve()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a60fa6579eab0db3c1c0ab1bf6d651be3">sieve_of_eratosthenes.cpp</a>
</li>
<li>Sieve()
: <a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a>
</li>
<li>sieve()
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a60fa6579eab0db3c1c0ab1bf6d651be3">sieve_of_eratosthenes.cpp</a>
</li>
<li>SieveOfEratosthenes()
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</li>
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<li>stack_idx
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</li>
<li>Standard_InvSqrt()
: <a class="el" href="d6/db8/inv__sqrt_8cpp.html#aa2703e5cf3fecde8becd9066b9666b97">inv_sqrt.cpp</a>
</li>
<li>struzik_search()
: <a class="el" href="d8/d8a/exponential__search_8cpp.html#a67e9c84b4e2eb30e3c5170eabfbb363d">exponential_search.cpp</a>
</li>

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globals_t.html
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namespacemembers.html
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<li>quadraticProbe()
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</li>
<li>quicksort()
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</li>
<li>quickSort()
: <a class="el" href="d5/d91/namespacesorting.html#a50b66a1c652291b9a346ec7342967178">sorting</a>
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<li>quicksort()
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namespacemembers_func.html
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@@ -354,12 +354,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
<li>quadraticProbe()
: <a class="el" href="d4/dd2/namespacequadratic__probing.html#ab431981b54c0bae1b2956f716aee1dcf">quadratic_probing</a>
</li>
<li>quicksort()
: <a class="el" href="d5/d91/namespacesorting.html#a9f59fe72dacc1f1218ef3c303d843168">sorting</a>
</li>
<li>quickSort()
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