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<div class="headertitle"><div class="title">easter.cpp</div></div>
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<div class="contents">
<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/*</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> * @file</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * @brief Determines the [Date of</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * Easter](https://en.wikipedia.org/wiki/Date_of_Easter) after 1582</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> *</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * @details</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> * The date of Easter is determined in each year through a calculation known as</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * &quot;computus.&quot; Easter is celebrated on the first Sunday after the Paschal full</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> * moon, which is the first full moon on or after 21 March. Determining this</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * date in advance requires a correlation between the lunar months and the solar</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> * year, while also accounting for the month, date, and weekday of the Julian or</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * Gregorian calendar. The complexity of the algorithm arises because of the</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> * desire to associate the date of Easter with the date of the Jewish feast of</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> * Passover which, Christians believe, is when Jesus was crucified.</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> *</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> *</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> * @author [AlternateWalls](https://github.com/AlternateWalls)</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"> */</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">/*</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment"> * @brief Contains information for Easter date</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment"> */</span></div>
<div class="foldopen" id="foldopen00027" data-start="{" data-end="};">
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"><a class="line" href="../../d1/df6/class_easter_year_month_day.html"> 27</a></span><span class="keyword">class </span>EasterYearMonthDay {</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="../../d1/df6/class_easter_year_month_day.html#a28d3cd09391390250932b7fb58fe61dc"> 29</a></span> uint64_t <a class="code hl_variable" href="../../d1/df6/class_easter_year_month_day.html#a28d3cd09391390250932b7fb58fe61dc">year</a>; </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="../../d1/df6/class_easter_year_month_day.html#a01a068eae0b6fa8f86f5f60c2840bbde"> 30</a></span> uint64_t <a class="code hl_variable" href="../../d1/df6/class_easter_year_month_day.html#a01a068eae0b6fa8f86f5f60c2840bbde">month</a>; </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="../../d1/df6/class_easter_year_month_day.html#ade0b934e5b1af24e19ff959673b2ec51"> 31</a></span> uint64_t <a class="code hl_variable" href="../../d1/df6/class_easter_year_month_day.html#ade0b934e5b1af24e19ff959673b2ec51">day</a>; </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> EasterYearMonthDay(uint64_t newYear, uint64_t newMonth, uint64_t newDay) {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <a class="code hl_variable" href="../../d1/df6/class_easter_year_month_day.html#a28d3cd09391390250932b7fb58fe61dc">year</a> = newYear; <span class="comment">// Assigns year to class</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_variable" href="../../d1/df6/class_easter_year_month_day.html#a01a068eae0b6fa8f86f5f60c2840bbde">month</a> = newMonth;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <a class="code hl_variable" href="../../d1/df6/class_easter_year_month_day.html#ade0b934e5b1af24e19ff959673b2ec51">day</a> = newDay;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>};</div>
</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">/*</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment"> * @brief Function that finds the month and day of Easter</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment"> * @params param1 An int &quot;y&quot; of the year you want to find Easter on after</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment"> * 1582</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment"> * @returns An instance of the easterYearMonthDay calss that contains the</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment"> * information (Ex. 420 - 4/20 or April 20th)</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment"> */</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><a class="code hl_class" href="../../d1/df6/class_easter_year_month_day.html">EasterYearMonthDay</a> findEaster(uint64_t y) {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">if</span> (y &gt; 1582) {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> uint64_t a = y % 19; <span class="comment">// Year&#39;s location on Metonic Calendar</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> uint64_t b = y / 100; <span class="comment">// Century index</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> uint64_t c = y % 100;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> uint64_t d = b / 4;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> uint64_t e = b % 4; <span class="comment">// Takes into account leap years</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> uint64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> = (b + 8) / 25;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> uint64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = (b - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> + 1) / 3;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> uint64_t <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = (19 * a + b - d - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> + 15) %</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> 30; <span class="comment">// Days from Mar. 21st until the full moon</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> uint64_t i = c / 4;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> uint64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> = c % 4;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> uint64_t r =</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> (32 + 2 * e + 2 * i - <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>) %</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> 7; <span class="comment">// The number of days from Paschal full moon to next Sunday</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> uint64_t m = (a + 11 * <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> + 22 * r) / 451;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> uint64_t n = (<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> + r - 7 * m + 114) / 31; <span class="comment">// Month of Easter</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> uint64_t p = (<a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> + r - 7 * m + 114) % 31; <span class="comment">// p + 1 is the day of Easter</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// Assign values</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_class" href="../../d1/df6/class_easter_year_month_day.html">EasterYearMonthDay</a> date(</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> y, n, p + 1); <span class="comment">// Assign values to new instance of class</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// Return date</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">return</span> date;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <a class="code hl_class" href="../../d1/df6/class_easter_year_month_day.html">EasterYearMonthDay</a> date(0, 0, 0);</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// Return date</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> date;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span>}</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// 2003 | April 20th</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> assert(findEaster(2003).month == 4); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> assert(findEaster(2003).day == 20); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// 1910 | March 27th</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> assert(findEaster(1910).month == 3); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> assert(findEaster(1910).day == 27); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// 1877 | April 1st</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> assert(findEaster(1877).month != 3); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> assert(findEaster(1877).day != 22); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// 1400 | Invalid date</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> assert(findEaster(1400).month == 0); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> assert(findEaster(1400).day == 0); <span class="comment">// Should return true</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span>}</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span>}</div>
<div class="ttc" id="aclass_easter_year_month_day_html"><div class="ttname"><a href="../../d1/df6/class_easter_year_month_day.html">EasterYearMonthDay</a></div><div class="ttdoc">for assert</div><div class="ttdef"><b>Definition</b> <a href="#l00027">easter.cpp:27</a></div></div>
<div class="ttc" id="aclass_easter_year_month_day_html_a01a068eae0b6fa8f86f5f60c2840bbde"><div class="ttname"><a href="../../d1/df6/class_easter_year_month_day.html#a01a068eae0b6fa8f86f5f60c2840bbde">EasterYearMonthDay::month</a></div><div class="ttdeci">uint64_t month</div><div class="ttdoc">month Easter is on</div><div class="ttdef"><b>Definition</b> <a href="#l00030">easter.cpp:30</a></div></div>
<div class="ttc" id="aclass_easter_year_month_day_html_a28d3cd09391390250932b7fb58fe61dc"><div class="ttname"><a href="../../d1/df6/class_easter_year_month_day.html#a28d3cd09391390250932b7fb58fe61dc">EasterYearMonthDay::year</a></div><div class="ttdeci">uint64_t year</div><div class="ttdoc">year Easter is on</div><div class="ttdef"><b>Definition</b> <a href="#l00029">easter.cpp:29</a></div></div>
<div class="ttc" id="aclass_easter_year_month_day_html_ade0b934e5b1af24e19ff959673b2ec51"><div class="ttname"><a href="../../d1/df6/class_easter_year_month_day.html#ade0b934e5b1af24e19ff959673b2ec51">EasterYearMonthDay::day</a></div><div class="ttdeci">uint64_t day</div><div class="ttdoc">day Easter is on</div><div class="ttdef"><b>Definition</b> <a href="#l00031">easter.cpp:31</a></div></div>
<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> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00115">composite_simpson_rule.cpp:115</a></div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00113">composite_simpson_rule.cpp:113</a></div></div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00082">generate_parentheses.cpp:82</a></div></div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition</b> <a href="../../d1/df3/hash__search_8cpp_source.html#l00045">hash_search.cpp:45</a></div></div>
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