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<div class="headertitle"><div class="title">approximate_pi.cpp File Reference</div></div>
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<p>Implementation to calculate an estimate of the <a href="https://en.wikipedia.org/wiki/File:Pi_30K.gif" target="_blank">number π (Pi)</a>.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for approximate_pi.cpp:</div>
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<p><a href="../../d0/d51/approximate__pi_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
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Namespaces</h2></td></tr>
<tr class="memitem:math" id="r_math"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <br /></td></tr>
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Typedefs</h2></td></tr>
<tr class="memitem:a006c8ebd11bb1e035815dc835a1a7a85" id="r_a006c8ebd11bb1e035815dc835a1a7a85"><td class="memItemLeft" align="right" valign="top">using&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a006c8ebd11bb1e035815dc835a1a7a85">math::Point</a></td></tr>
<tr class="memdesc:a006c8ebd11bb1e035815dc835a1a7a85"><td class="mdescLeft">&#160;</td><td class="mdescRight">structure of points containing two numbers, x and y, such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:abf7f2a6d91f1ca6c89698792aea3f188" id="r_abf7f2a6d91f1ca6c89698792aea3f188"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a> (const std::vector&lt; <a class="el" href="../../dd/d47/namespacemath.html#a006c8ebd11bb1e035815dc835a1a7a85">Point</a> &gt; &amp;pts)</td></tr>
<tr class="memdesc:abf7f2a6d91f1ca6c89698792aea3f188"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function uses the points in a given vector 'pts' (drawn at random) to return an approximation of the number π. <br /></td></tr>
<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e" id="r_a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation to calculate an estimate of the <a href="https://en.wikipedia.org/wiki/File:Pi_30K.gif" target="_blank">number π (Pi)</a>. </p>
<p>We take a random point P with coordinates (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. If x² + y² ≤ 1, then the point is inside the quarter disk of radius 1, else the point is outside. We know that the probability of the point being inside the quarter disk is equal to π/4 double approx(vector&lt;Point&gt; &amp;pts) which will use the points pts (drawn at random) to return an estimate of the number π </p><dl class="section note"><dt>Note</dt><dd>This implementation is better than naive recursive or iterative approach.</dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Qannaf" target="_blank">Qannaf AL-SAHMI</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d0/d51/approximate__pi_8cpp_source.html">approximate_pi.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d0/d51/approximate__pi_8cpp_source.html#l00080">80</a> of file <a class="el" href="../../d0/d51/approximate__pi_8cpp_source.html">approximate_pi.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 80</span> {</div>
<div class="line"><span class="lineno"> 81</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 83</span>}</div>
<div class="ttc" id="aapproximate__pi_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../d0/d51/approximate__pi_8cpp_source.html#l00062">approximate_pi.cpp:62</a></div></div>
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<a id="a483bb8ccf42aaf7375a83e91490eda1e" name="a483bb8ccf42aaf7375a83e91490eda1e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">void tests </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d0/d51/approximate__pi_8cpp_source.html#l00062">62</a> of file <a class="el" href="../../d0/d51/approximate__pi_8cpp_source.html">approximate_pi.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</span> std::vector&lt;math::Point&gt; rands;</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">for</span> (std::size_t i = 0; i &lt; 100000; i++) {</div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_typedef" href="../../dd/d47/namespacemath.html#a006c8ebd11bb1e035815dc835a1a7a85">math::Point</a> p;</div>
<div class="line"><span class="lineno"> 66</span> p.x = rand() / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(RAND_MAX); <span class="comment">// 0 &lt;= x &lt;= 1</span></div>
<div class="line"><span class="lineno"> 67</span> p.y = rand() / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(RAND_MAX); <span class="comment">// 0 &lt;= y &lt;= 1</span></div>
<div class="line"><span class="lineno"> 68</span> rands.push_back(p);</div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a>(rands) &gt; 3.135);</div>
<div class="line"><span class="lineno"> 71</span> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a>(rands) &lt; 3.145);</div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> std::cout &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 74</span>}</div>
<div class="ttc" id="anamespacemath_html_a006c8ebd11bb1e035815dc835a1a7a85"><div class="ttname"><a href="../../dd/d47/namespacemath.html#a006c8ebd11bb1e035815dc835a1a7a85">math::Point</a></div><div class="ttdeci">struct { double x; double y;} Point</div><div class="ttdoc">structure of points containing two numbers, x and y, such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1.</div><div class="ttdef"><b>Definition</b> <a href="../../d0/d51/approximate__pi_8cpp_source.html#l00035">approximate_pi.cpp:35</a></div></div>
<div class="ttc" id="anamespacemath_html_abf7f2a6d91f1ca6c89698792aea3f188"><div class="ttname"><a href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a></div><div class="ttdeci">double approximate_pi(const std::vector&lt; Point &gt; &amp;pts)</div><div class="ttdoc">This function uses the points in a given vector &#39;pts&#39; (drawn at random) to return an approximation of...</div><div class="ttdef"><b>Definition</b> <a href="../../d0/d51/approximate__pi_8cpp_source.html#l00047">approximate_pi.cpp:47</a></div></div>
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