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<p>C++ Program for Modular Exponentiation Iteratively.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for modular_exponentiation.cpp:</div>
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<tr class="memitem:dd/d47/namespacemath"><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 M_PI definition and pow() <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:afcd07701d73ed65cd616bcba02737f3d"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a> (uint64_t a, uint64_t b, uint64_t c)</td></tr>
<tr class="memdesc:afcd07701d73ed65cd616bcba02737f3d"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function calculates a raised to exponent b under modulo c using modular exponentiation. <a href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">More...</a><br /></td></tr>
<tr class="separator:afcd07701d73ed65cd616bcba02737f3d"><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="../../d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d6d/modular__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d0/d6d/modular__exponentiation_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 >C++ Program for Modular Exponentiation Iteratively. </p>
<p >The task is to calculate the value of an integer a raised to an integer exponent b under modulo c. </p><dl class="section note"><dt>Note</dt><dd>The time complexity of this approach is O(log b).</dd></dl>
<p>Example: (4^3) % 5 (where ^ stands for exponentiation and % for modulo) (4*4*4) % 5 (4 % 5) * ( (4*4) % 5 ) 4 * (16 % 5) 4 * 1 4 We can also verify the result as 4^3 is 64 and 64 modulo 5 is 4</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Shri2206" target="_blank">Shri2206</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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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>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> {</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <a class="code hl_function" href="../../d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>}</div>
<div class="ttc" id="amodular__exponentiation_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition:</b> modular_exponentiation.cpp:60</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 >Function for testing power function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<div class="fragment"><div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> uint32_t test_case_1 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a>(2, 5, 13);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> assert(test_case_1 == 6);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</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;Test 1 Passed!&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="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> uint32_t test_case_2 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a>(14, 7, 15);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> assert(test_case_2 == 14);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</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;Test 2 Passed!&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="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> uint64_t test_case_3 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a>(8, 15, 41);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> assert(test_case_3 == 32);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</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;Test 3 Passed!&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="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> uint64_t test_case_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a>(27, 2, 5);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> assert(test_case_4 == 4);</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/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 4 Passed!&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="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> uint16_t test_case_5 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a>(7, 3, 6);</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> assert(test_case_5 == 1);</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/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 5 Passed!&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="l00080" name="l00080"></a><span class="lineno"> 80</span>}</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>
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<div class="ttc" id="anamespacemath_html_afcd07701d73ed65cd616bcba02737f3d"><div class="ttname"><a href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">math::power</a></div><div class="ttdeci">uint64_t power(uint64_t a, uint64_t b, uint64_t c)</div><div class="ttdoc">This function calculates a raised to exponent b under modulo c using modular exponentiation.</div><div class="ttdef"><b>Definition:</b> modular_exponentiation.cpp:35</div></div>
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