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<div class="headertitle"><div class="title">modular_exponentiation.cpp</div></div>
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<div class="contents">
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<a href="../../d0/d6d/modular__exponentiation_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
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<div class="foldopen" id="foldopen00035" data-start="{" data-end="}">
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"><a class="line" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d"> 35</a></span>uint64_t <a class="code hl_function" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a>(uint64_t a, uint64_t b, uint64_t c) {</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> uint64_t ans = 1; </div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> a = a % c; </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> (a == 0) {</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">return</span> 0; </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">while</span> (b > 0) {</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (b & 1) {</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> ans = ((ans % c) * (a % c)) % c;</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> b = b >> 1; </div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> a = ((a % c) * (a % c)) % c;</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">return</span> ans;</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span>}</div>
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</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span>} <span class="comment">// namespace math</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span></div>
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<div class="foldopen" id="foldopen00060" data-start="{" data-end="}">
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"><a class="line" href="../../d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 60</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d0/d6d/modular__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
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<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>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> assert(test_case_1 == 6);</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> std::cout << <span class="stringliteral">"Test 1 Passed!"</span> << std::endl;</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<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>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> assert(test_case_2 == 14);</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> std::cout << <span class="stringliteral">"Test 2 Passed!"</span> << std::endl;</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
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<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>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> assert(test_case_3 == 32);</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> std::cout << <span class="stringliteral">"Test 3 Passed!"</span> << std::endl;</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
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<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>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> assert(test_case_4 == 4);</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> std::cout << <span class="stringliteral">"Test 4 Passed!"</span> << std::endl;</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
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<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>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> assert(test_case_5 == 1);</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> std::cout << <span class="stringliteral">"Test 5 Passed!"</span> << std::endl;</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>}</div>
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</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span></div>
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<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="../../d0/d6d/modular__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 86</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d0/d6d/modular__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<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>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>}</div>
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</div>
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<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> <a href="#l00060">modular_exponentiation.cpp:60</a></div></div>
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<div class="ttc" id="amodular__exponentiation_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d0/d6d/modular__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00086">modular_exponentiation.cpp:86</a></div></div>
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<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for assert</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> <a href="#l00035">modular_exponentiation.cpp:35</a></div></div>
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