Add computus in C++ (algorithm-archivists#703)

Author: VincentZalzal

contents/computus/code/c++/gauss_easter.cpp

@@ -0,0 +1,60 @@
+#include <iostream>
+#include <string>
+
+std::string computus(int year, bool servois = false) {
+  // Year's position on the 19 year metonic cycle
+  int a = year % 19;
+
+  // Century index
+  int k = year / 100;
+
+  // Shift of metonic cycle, add a day offset every 300 years
+  int p = (13 + 8 * k) / 25;
+
+  // Correction for non-observed leap days
+  int q = k / 4;
+
+  // Correction to starting point of calculation each century
+  int M = (15 - p + k - q) % 30;
+
+  // Number of days from March 21st until the full moon
+  int d = (19 * a + M) % 30;
+
+  // Returning if user wants value for Servois' table
+  if (servois) {
+    return std::to_string((21 + d) % 31);
+  }
+
+  // Finding the next Sunday
+  // Century-based offset in weekly calculation
+  int N = (4 + k - q) % 7;
+
+  // Correction for leap days
+  int b = year % 4;
+  int c = year % 7;
+
+  // Days from d to next Sunday
+  int e = (2 * b + 4 * c + 6 * d + N) % 7;
+
+  // Historical corrections for April 26 and 25
+  if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {
+    e = -1;
+  }
+
+  // Determination of the correct month for Easter
+  return 22 + d + e > 31 ? "April " + std::to_string(d + e - 9)
+                         : "March " + std::to_string(22 + d + e);
+}
+
+// Here, we will output the date of the Paschal full moon (using Servois
+// notation), and Easter for 2020-2030
+int main() {
+  std::cout << "The following are the dates of the Paschal full moon (using "
+               "Servois notation) and the date of Easter for 2020-2030 AD:\n"
+               "Year\tServois number\tEaster\n";
+
+  for (int year = 2020; year <= 2030; year++) {
+    std::cout << year << "\t\t" << computus(year, true) << '\t'
+              << computus(year) << std::endl;
+  }
+}

contents/computus/computus.md

@@ -287,6 +287,8 @@ For now, we have the code outputting a tuple of $$d$$ and $$e$$, so users can us
 [import, lang:"crystal"](code/crystal/gauss_easter.cr)
 {% sample lang="c" %}
 [import, lang:"c"](code/c/gauss_easter.c)
+{% sample lang="cpp" %}
+[import, lang:"cpp"](code/c++/gauss_easter.cpp)
 {% endmethod %}