Add Computus in Nim (#780)

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 %}