Add Computus in Nim (algorithm-archivists#780)

Author: berquist

contents/computus/code/nim/gauss_easter.nim

@@ -0,0 +1,45 @@
+import strformat
+
+func computus(year: int, servois: bool = false): string =
+  let
+    # Year's position on the 19 year metonic cycle
+    a = year mod 19
+    # Century index
+    k = year div 100
+    # Shift of metonic cycle, add a day offset every 300 years
+    p = (13 + 8 * k) div 25
+    # Correction for non-observed leap days
+    q = k div 4
+    # Correction to starting point of calculation each century
+    m = (15 - p + k - q) mod 30
+    # Number of days from March 21st until the full moon
+    d = (19 * a + m) mod 30
+  # Returning of user wants value for Servois' table
+  if servois:
+    return $((21 + d) mod 31)
+  let
+    # Find the next Sunday
+    # Century-based offset in weekly calculation
+    n = (4 + k - q) mod 7
+    # Correction for leap days
+    b = year mod 4
+    c = year mod 7
+    # Days from d to next Sunday
+    temp_e = (2 * b + 4 * c + 6 * d + n) mod 7
+    # Historical corrections for April 26 and 25
+    e = if (d == 29 and temp_e == 6) or (d == 28 and temp_e == 6 and a > 10):
+          -1
+        else:
+          temp_e
+  # Determination of the correct month for Easter
+  if (22 + d + e) > 31:
+    result = "April {d + e - 9}".fmt
+  else:
+    result = "March {22 + d + e}".fmt
+
+when isMainModule:
+  echo "The following are the dates of the Paschal full moon (using Servois "
+  echo "notation) and the date of Easter for 2020-2030 AD:"
+  echo "Year Servois number Easter"
+  for year in 2020..2030:
+    echo "{year} {computus(year, true):14} {computus(year, false):6}".fmt

contents/computus/computus.md

@@ -297,6 +297,8 @@ For now, we have the code outputting a tuple of $$d$$ and $$e$$, so users can us
 [import, lang:"cpp"](code/c++/gauss_easter.cpp)
 {% sample lang="lisp" %}
 [import, lang:"lisp"](code/clisp/gauss-easter.lisp)
+{% sample lang="nim" %}
+[import, lang:"nim"](code/nim/gauss_easter.nim)
 {% endmethod %}