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<title>Algorithms_in_C++: others/primality_test.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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</div>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -116,7 +116,7 @@ Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Primality_test" target="_blank">Primality test</a> implementation. </p>
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<p >A simple and efficient implementation of a function to test if a number is prime, based on the fact that </p><blockquote class="doxtable">
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<p >Every Prime number, except 2 and 3, are of the form \(6k\pm1\) for integer values of k. </p>
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<p >‍Every Prime number, except 2 and 3, are of the form \(6k\pm1\) for integer values of k. </p>
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</blockquote>
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<p>This gives a 3x speed improvement. </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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@@ -142,17 +142,17 @@ Functions</h2></td></tr>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>true if prime else false </dd></dl>
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<div class="fragment"><div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> {</div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keywordflow">if</span> (((!(number & 1)) && number != 2) || (number < 2) ||</div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> (number % 3 == 0 && number != 3))</div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; 36 * <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> * <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 12 * <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> < number; ++<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>) {</div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">if</span> ((number % (6 * k + 1) == 0) || (number % (6 * k - 1) == 0))</div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> }</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 18</span> {</div>
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<div class="line"><span class="lineno"> 19</span> <span class="keywordflow">if</span> (((!(number & 1)) && number != 2) || (number < 2) ||</div>
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<div class="line"><span class="lineno"> 20</span> (number % 3 == 0 && number != 3))</div>
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<div class="line"><span class="lineno"> 21</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 22</span> </div>
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<div class="line"><span class="lineno"> 23</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; 36 * <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> * <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> - 12 * <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> < number; ++<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>) {</div>
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<div class="line"><span class="lineno"> 24</span> <span class="keywordflow">if</span> ((number % (6 * k + 1) == 0) || (number % (6 * k - 1) == 0))</div>
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<div class="line"><span class="lineno"> 25</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 26</span> }</div>
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<div class="line"><span class="lineno"> 27</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 28</span>}</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
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</div><!-- fragment -->
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</div>
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@@ -173,18 +173,18 @@ Functions</h2></td></tr>
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</table>
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</div><div class="memdoc">
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<p >main function </p>
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<div class="fragment"><div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> {</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// Main Function</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter the value of n to check if Prime\n"</span>;</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordtype">int</span> n;</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> n;</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">IsPrime</a>(n))</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << n << <span class="stringliteral">" is Prime"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">else</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << n << <span class="stringliteral">" is not Prime"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 31</span> {</div>
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<div class="line"><span class="lineno"> 32</span> <span class="comment">// Main Function</span></div>
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<div class="line"><span class="lineno"> 33</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Enter the value of n to check if Prime\n"</span>;</div>
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<div class="line"><span class="lineno"> 34</span> <span class="keywordtype">int</span> n;</div>
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<div class="line"><span class="lineno"> 35</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> n;</div>
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<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">IsPrime</a>(n))</div>
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<div class="line"><span class="lineno"> 37</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << n << <span class="stringliteral">" is Prime"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 38</span> <span class="keywordflow">else</span></div>
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<div class="line"><span class="lineno"> 39</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << n << <span class="stringliteral">" is not Prime"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 40</span> </div>
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<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 42</span>}</div>
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<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<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>
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<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>
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@@ -204,7 +204,7 @@ Here is the call graph for this function:</div>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
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