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<div class="headertitle"><div class="title">sieve_of_eratosthenes.cpp File Reference</div></div>
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</div><!--header-->
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<div class="contents">
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<p>Prime Numbers using <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" target="_blank">Sieve of Eratosthenes</a>
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cstdint></code><br />
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<code>#include <cassert></code><br />
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<code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for sieve_of_eratosthenes.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" loading="lazy" frameborder="0" src="../../da/d35/sieve__of__eratosthenes_8cpp__incl.svg" width="336" height="111"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<p><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:math" id="r_math"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft"> </td><td class="mdescRight">for assert <br /></td></tr>
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<tr class="memitem:sieve_5Fof_5Feratosthenes" id="r_sieve_5Fof_5Feratosthenes"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/db0/namespacesieve__of__eratosthenes.html">sieve_of_eratosthenes</a></td></tr>
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<tr class="memdesc:d2/db0/namespacesieve__of__eratosthenes"><td class="mdescLeft"> </td><td class="mdescRight">Functions for finding Prime Numbers using Sieve of Eratosthenes. <br /></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a22be949d160b26361f7e323310f7fa0c" id="r_a22be949d160b26361f7e323310f7fa0c"><td class="memItemLeft" align="right" valign="top">std::vector< bool > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a> (uint32_t N)</td></tr>
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<tr class="memdesc:a22be949d160b26361f7e323310f7fa0c"><td class="mdescLeft"> </td><td class="mdescRight">Function to sieve out the primes. <br /></td></tr>
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<tr class="memitem:a55bc4a221e584d33b79b322432ecc0f3" id="r_a55bc4a221e584d33b79b322432ecc0f3"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a55bc4a221e584d33b79b322432ecc0f3">math::sieve_of_eratosthenes::print</a> (uint32_t N, const std::vector< bool > &<a class="el" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>)</td></tr>
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<tr class="memdesc:a55bc4a221e584d33b79b322432ecc0f3"><td class="mdescLeft"> </td><td class="mdescRight">Function to print the prime numbers. <br /></td></tr>
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<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e" id="r_a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
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<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft"> </td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
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</table>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Prime Numbers using <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" target="_blank">Sieve of Eratosthenes</a> </p>
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<p>Sieve of Eratosthenes is an algorithm that finds all the primes between 2 and N.</p>
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<p>Time Complexity : \(O(N \cdot\log \log N)\) <br />
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Space Complexity : \(O(N)\)</p>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html" title="Compute prime numbers upto 1 billion.">primes_up_to_billion.cpp</a> <a class="el" href="../../de/d9b/prime__numbers_8cpp.html" title="Get list of prime numbers.">prime_numbers.cpp</a> </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html">sieve_of_eratosthenes.cpp</a>.</p>
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</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memitem">
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td></td>
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<p>Main function. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html#l00119">119</a> of file <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html">sieve_of_eratosthenes.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 119</span> {</div>
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<div class="line"><span class="lineno"> 120</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();</div>
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<div class="line"><span class="lineno"> 121</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 122</span>}</div>
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<div class="ttc" id="asieve__of__eratosthenes_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="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html#l00081">sieve_of_eratosthenes.cpp:81</a></div></div>
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</div><!-- fragment -->
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</div>
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<a id="a55bc4a221e584d33b79b322432ecc0f3" name="a55bc4a221e584d33b79b322432ecc0f3"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a55bc4a221e584d33b79b322432ecc0f3">◆ </a></span>print()</h2>
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<td class="memname">void math::sieve_of_eratosthenes::print </td>
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<td>(</td>
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<td class="paramtype">uint32_t</td> <td class="paramname"><span class="paramname"><em>N</em></span>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const std::vector< bool > &</td> <td class="paramname"><span class="paramname"><em>is_prime</em></span> )</td>
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<p>Function to print the prime numbers. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">N</td><td>number till which primes are to be found </td></tr>
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<tr><td class="paramname">is_prime</td><td>a vector of <span class="tt">N + 1</span> booleans identifying if <span class="tt">i</span>^th number is a prime or not </td></tr>
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</table>
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</dd>
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</dl>
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<p class="definition">Definition at line <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html#l00065">65</a> of file <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html">sieve_of_eratosthenes.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 65</span> {</div>
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<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">for</span> (uint32_t i = 2; i <= N; i++) {</div>
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<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[i]) {</div>
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<div class="line"><span class="lineno"> 68</span> std::cout << i << <span class="charliteral">' '</span>;</div>
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<div class="line"><span class="lineno"> 69</span> }</div>
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<div class="line"><span class="lineno"> 70</span> }</div>
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<div class="line"><span class="lineno"> 71</span> std::cout << std::endl;</div>
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<div class="line"><span class="lineno"> 72</span>}</div>
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<div class="ttc" id="anamespacemath_html_abd8f794b2229b42876169ff841b6e444"><div class="ttname"><a href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">math::is_prime</a></div><div class="ttdeci">bool is_prime(int64_t num)</div><div class="ttdoc">Function to check if the given number is prime or not.</div><div class="ttdef"><b>Definition</b> <a href="../../db/d93/check__prime_8cpp_source.html#l00031">check_prime.cpp:31</a></div></div>
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</div><!-- fragment -->
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</div>
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<a id="a22be949d160b26361f7e323310f7fa0c" name="a22be949d160b26361f7e323310f7fa0c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a22be949d160b26361f7e323310f7fa0c">◆ </a></span>sieve()</h2>
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<td class="memname">std::vector< bool > math::sieve_of_eratosthenes::sieve </td>
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<td>(</td>
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<td class="paramtype">uint32_t</td> <td class="paramname"><span class="paramname"><em>N</em></span></td><td>)</td>
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<td></td>
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<p>Function to sieve out the primes. </p>
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<p>This function finds all the primes between 2 and N using the Sieve of Eratosthenes algorithm. It starts by assuming all numbers (except zero and one) are prime and then iteratively marks the multiples of each prime as non-prime.</p>
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<p>Contains a common optimization to start eliminating multiples of a prime p starting from p * p since all of the lower multiples have been already eliminated. </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">N</td><td>number till which primes are to be found </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>is_prime a vector of <span class="tt">N + 1</span> booleans identifying if <span class="tt">i</span>^th number is a prime or not </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html#l00045">45</a> of file <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html">sieve_of_eratosthenes.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 45</span> {</div>
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<div class="line"><span class="lineno"> 46</span> std::vector<bool> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>(N + 1, <span class="keyword">true</span>); <span class="comment">// Initialize all as prime numbers</span></div>
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<div class="line"><span class="lineno"> 47</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[0] = <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[1] = <span class="keyword">false</span>; <span class="comment">// 0 and 1 are not prime numbers</span></div>
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<div class="line"><span class="lineno"> 48</span> </div>
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<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">for</span> (uint32_t i = 2; i * i <= N; i++) {</div>
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<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[i]) {</div>
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<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (uint32_t j = i * i; j <= N; j += i) {</div>
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<div class="line"><span class="lineno"> 52</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[j] = <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 53</span> }</div>
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<div class="line"><span class="lineno"> 54</span> }</div>
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<div class="line"><span class="lineno"> 55</span> }</div>
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<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>;</div>
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<div class="line"><span class="lineno"> 57</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">◆ </a></span>tests()</h2>
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<td class="memname">void tests </td>
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<td>(</td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>Self-test implementations. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html#l00081">81</a> of file <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html">sieve_of_eratosthenes.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
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<div class="line"><span class="lineno"> 82</span> std::vector<bool> is_prime_1 =</div>
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<div class="line"><span class="lineno"> 83</span> <a class="code hl_function" href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a>(<span class="keyword">static_cast<</span>uint32_t<span class="keyword">></span>(10));</div>
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<div class="line"><span class="lineno"> 84</span> std::vector<bool> is_prime_2 =</div>
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<div class="line"><span class="lineno"> 85</span> <a class="code hl_function" href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a>(<span class="keyword">static_cast<</span>uint32_t<span class="keyword">></span>(20));</div>
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<div class="line"><span class="lineno"> 86</span> std::vector<bool> is_prime_3 =</div>
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<div class="line"><span class="lineno"> 87</span> <a class="code hl_function" href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a>(<span class="keyword">static_cast<</span>uint32_t<span class="keyword">></span>(100));</div>
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<div class="line"><span class="lineno"> 88</span> </div>
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<div class="line"><span class="lineno"> 89</span> std::vector<bool> expected_1{<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 90</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>};</div>
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<div class="line"><span class="lineno"> 91</span> assert(is_prime_1 == expected_1);</div>
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<div class="line"><span class="lineno"> 92</span> </div>
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<div class="line"><span class="lineno"> 93</span> std::vector<bool> expected_2{<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 94</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 95</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 96</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>};</div>
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<div class="line"><span class="lineno"> 97</span> assert(is_prime_2 == expected_2);</div>
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<div class="line"><span class="lineno"> 98</span> </div>
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<div class="line"><span class="lineno"> 99</span> std::vector<bool> expected_3{</div>
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<div class="line"><span class="lineno"> 100</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
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<div class="line"><span class="lineno"> 101</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 102</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 103</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
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<div class="line"><span class="lineno"> 104</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
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<div class="line"><span class="lineno"> 105</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 106</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
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<div class="line"><span class="lineno"> 107</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 108</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
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<div class="line"><span class="lineno"> 109</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
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<div class="line"><span class="lineno"> 110</span> <span class="keyword">false</span>};</div>
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<div class="line"><span class="lineno"> 111</span> assert(is_prime_3 == expected_3);</div>
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<div class="line"><span class="lineno"> 112</span> </div>
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<div class="line"><span class="lineno"> 113</span>}</div>
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<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a22be949d160b26361f7e323310f7fa0c"><div class="ttname"><a href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a></div><div class="ttdeci">std::vector< bool > sieve(uint32_t N)</div><div class="ttdoc">Function to sieve out the primes.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/ddf/sieve__of__eratosthenes_8cpp_source.html#l00045">sieve_of_eratosthenes.cpp:45</a></div></div>
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