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Documentation for c6af943508
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realstealthninja
@@ -114,17 +114,18 @@ $(function(){initNavTree('df/d72/modular__division_8cpp.html','../../'); initRes
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<p>An algorithm to divide two numbers under modulo p <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a>
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <cstdint></code><br />
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<code>#include <iostream></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for modular_division.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/dcc/modular__division_8cpp__incl.svg" width="187" 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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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/dcc/modular__division_8cpp__incl.svg" width="255" 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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</div>
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</div><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:"><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 IO operations <br /></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="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d64/namespacemodular__division.html">modular_division</a></td></tr>
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<tr class="memdesc:d1/d64/namespacemodular__division"><td class="mdescLeft"> </td><td class="mdescRight">Functions for <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a> implementation. <br /></td></tr>
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@@ -177,11 +178,11 @@ 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>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 112</span> {</div>
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<div class="line"><span class="lineno"> 113</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
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<div class="line"><span class="lineno"> 114</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 115</span>}</div>
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<div class="ttc" id="amodular__division_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> modular_division.cpp:88</div></div>
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<div class="fragment"><div class="line"><span class="lineno"> 113</span> {</div>
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<div class="line"><span class="lineno"> 114</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
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<div class="line"><span class="lineno"> 115</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 116</span>}</div>
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<div class="ttc" id="amodular__division_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> modular_division.cpp:89</div></div>
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Here is the call graph for this function:</div>
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@@ -226,13 +227,13 @@ Here is the call graph for this function:</div>
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<dl class="section return"><dt>Returns</dt><dd>a/b modulo c </dd></dl>
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<p>Calculate the inverse of b</p>
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<p>Calculate the final result</p>
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<div class="fragment"><div class="line"><span class="lineno"> 74</span> {</div>
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<div class="line"><span class="lineno"> 75</span> uint64_t inverse = <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>(b, p - 2, p) % p; <span class="comment">/// Calculate the inverse of b</span></div>
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<div class="line"><span class="lineno"> 76</span> uint64_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> =</div>
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<div class="line"><span class="lineno"> 77</span> ((a % p) * (inverse % p)) % p; <span class="comment">/// Calculate the final result</span></div>
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<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><span class="lineno"> 79</span>}</div>
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<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> fibonacci_sum.cpp:76</div></div>
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<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
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<div class="line"><span class="lineno"> 76</span> uint64_t inverse = <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>(b, p - 2, p) % p; <span class="comment">/// Calculate the inverse of b</span></div>
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<div class="line"><span class="lineno"> 77</span> uint64_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> =</div>
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<div class="line"><span class="lineno"> 78</span> ((a % p) * (inverse % p)) % p; <span class="comment">/// Calculate the final result</span></div>
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<div class="line"><span class="lineno"> 79</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><span class="lineno"> 80</span>}</div>
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<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> fibonacci_sum.cpp:77</div></div>
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<div class="ttc" id="apower__for__huge__numbers_8cpp_html_ae249a2af508aa94266023ce8aa81426f"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a></div><div class="ttdeci">void power(int x, int n)</div><div class="ttdef"><b>Definition</b> power_for_huge_numbers.cpp:56</div></div>
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</div><!-- fragment --><div class="dynheader">
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@@ -282,23 +283,23 @@ Here is the call graph for this function:</div>
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<p>If b is odd, multiply a with answer</p>
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<p>b must be even now</p>
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<p>b = b/2</p>
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<div class="fragment"><div class="line"><span class="lineno"> 49</span> {</div>
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<div class="line"><span class="lineno"> 50</span> uint64_t ans = 1; <span class="comment">/// Initialize the answer to be returned</span></div>
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<div class="line"><span class="lineno"> 51</span> a = a % c; <span class="comment">/// Update a if it is more than or equal to c</span></div>
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<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">if</span> (a == 0) {</div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> 0; <span class="comment">/// In case a is divisible by c;</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> <span class="keywordflow">while</span> (b > 0) {<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 56</span><span class="comment"> /// If b is odd, multiply a with answer</span></div>
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<div class="line"><span class="lineno"> 57</span><span class="comment"></span> <span class="keywordflow">if</span> (b & 1) {</div>
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<div class="line"><span class="lineno"> 58</span> ans = ((ans % c) * (a % c)) % c;</div>
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<div class="line"><span class="lineno"> 59</span> }<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 60</span><span class="comment"> /// b must be even now</span></div>
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<div class="line"><span class="lineno"> 61</span><span class="comment"></span> b = b >> 1; <span class="comment">/// b = b/2</span></div>
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<div class="line"><span class="lineno"> 62</span> a = ((a % c) * (a % c)) % c;</div>
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<div class="line"><span class="lineno"> 63</span> }</div>
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<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> ans;</div>
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<div class="line"><span class="lineno"> 65</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 50</span> {</div>
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<div class="line"><span class="lineno"> 51</span> uint64_t ans = 1; <span class="comment">/// Initialize the answer to be returned</span></div>
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<div class="line"><span class="lineno"> 52</span> a = a % c; <span class="comment">/// Update a if it is more than or equal to c</span></div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">if</span> (a == 0) {</div>
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<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">return</span> 0; <span class="comment">/// In case a is divisible by c;</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">while</span> (b > 0) {<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 57</span><span class="comment"> /// If b is odd, multiply a with answer</span></div>
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<div class="line"><span class="lineno"> 58</span><span class="comment"></span> <span class="keywordflow">if</span> (b & 1) {</div>
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<div class="line"><span class="lineno"> 59</span> ans = ((ans % c) * (a % c)) % c;</div>
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<div class="line"><span class="lineno"> 60</span> }<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 61</span><span class="comment"> /// b must be even now</span></div>
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<div class="line"><span class="lineno"> 62</span><span class="comment"></span> b = b >> 1; <span class="comment">/// b = b/2</span></div>
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<div class="line"><span class="lineno"> 63</span> a = ((a % c) * (a % c)) % c;</div>
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<div class="line"><span class="lineno"> 64</span> }</div>
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<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">return</span> ans;</div>
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<div class="line"><span class="lineno"> 66</span>}</div>
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</div><!-- fragment -->
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</div>
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</div>
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@@ -325,26 +326,26 @@ Here is the call graph for this function:</div>
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</table>
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</div><div class="memdoc">
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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>
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<div class="fragment"><div class="line"><span class="lineno"> 88</span> {</div>
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<div class="line"><span class="lineno"> 89</span> uint64_t test_case_1 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(8, 2, 2);</div>
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<div class="line"><span class="lineno"> 90</span> assert(test_case_1 == 0);</div>
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<div class="line"><span class="lineno"> 91</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">"Test 1 Passed!"</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"> 92</span> uint64_t test_case_2 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(15, 3, 7);</div>
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<div class="line"><span class="lineno"> 93</span> assert(test_case_2 == 5);</div>
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<div class="line"><span class="lineno"> 94</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">"Test 2 Passed!"</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"> 95</span> uint64_t test_case_3 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(10, 5, 2);</div>
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<div class="line"><span class="lineno"> 96</span> assert(test_case_3 == 0);</div>
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<div class="line"><span class="lineno"> 97</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">"Test 3 Passed!"</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"> 98</span> uint64_t test_case_4 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(81, 3, 5);</div>
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<div class="line"><span class="lineno"> 99</span> assert(test_case_4 == 2);</div>
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<div class="line"><span class="lineno"> 100</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">"Test 4 Passed!"</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"> 101</span> uint64_t test_case_5 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(12848, 73, 29);</div>
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<div class="line"><span class="lineno"> 102</span> assert(test_case_5 == 2);</div>
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<div class="line"><span class="lineno"> 103</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">"Test 5 Passed!"</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"> 104</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 89</span> {</div>
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<div class="line"><span class="lineno"> 90</span> uint64_t test_case_1 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(8, 2, 2);</div>
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<div class="line"><span class="lineno"> 91</span> assert(test_case_1 == 0);</div>
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<div class="line"><span class="lineno"> 92</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">"Test 1 Passed!"</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"> 93</span> uint64_t test_case_2 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(15, 3, 7);</div>
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<div class="line"><span class="lineno"> 94</span> assert(test_case_2 == 5);</div>
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<div class="line"><span class="lineno"> 95</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">"Test 2 Passed!"</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"> 96</span> uint64_t test_case_3 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(10, 5, 2);</div>
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<div class="line"><span class="lineno"> 97</span> assert(test_case_3 == 0);</div>
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<div class="line"><span class="lineno"> 98</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">"Test 3 Passed!"</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"> 99</span> uint64_t test_case_4 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(81, 3, 5);</div>
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<div class="line"><span class="lineno"> 100</span> assert(test_case_4 == 2);</div>
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<div class="line"><span class="lineno"> 101</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">"Test 4 Passed!"</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"> 102</span> uint64_t test_case_5 = <a class="code hl_function" href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a>(12848, 73, 29);</div>
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<div class="line"><span class="lineno"> 103</span> assert(test_case_5 == 2);</div>
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<div class="line"><span class="lineno"> 104</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">"Test 5 Passed!"</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"> 105</span>}</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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<div class="ttc" id="amodular__division_8cpp_html_a905e368ae121beb7e7ea35349ddcdac7"><div class="ttname"><a href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a></div><div class="ttdeci">uint64_t mod_division(uint64_t a, uint64_t b, uint64_t p)</div><div class="ttdoc">This function calculates modular division.</div><div class="ttdef"><b>Definition</b> modular_division.cpp:74</div></div>
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<div class="ttc" id="amodular__division_8cpp_html_a905e368ae121beb7e7ea35349ddcdac7"><div class="ttname"><a href="#a905e368ae121beb7e7ea35349ddcdac7">math::modular_division::mod_division</a></div><div class="ttdeci">uint64_t mod_division(uint64_t a, uint64_t b, uint64_t p)</div><div class="ttdoc">This function calculates modular division.</div><div class="ttdef"><b>Definition</b> modular_division.cpp:75</div></div>
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</div><!-- fragment --><div class="dynheader">
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