add a better method to calculate easter sunday

src/pylib/date.py

@@ -10,16 +10,58 @@
    
 .. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de>
 """
+import datetime
 
+def computus_anonymous_gregorian(year):
+  """Computus anonymous Gregorian algorithm or Meeus/Jones/Butcher
+  algorithm.
+
+  :param year: the year to calculate the Easter Sunday
+  :type year: int
+
+  :returns: the day of Easter Sunday
+  :rtype: datetime.date
+
+  For Gregorian calendar (1583 and onward)
+  Works without exeptions.
+
+  Published
+  1876 by Anonymous in Nature
+  1877 by Samuel Butcher in The Ecclesiastical Calendar
+  1916 by Arthur Downing in The Observatory
+  1922 by Harold Spencer Jones in General Astronomy
+  1988 by Peter Duffett-Smith in Practical Astronomy with your Calculator
+  1991 by Jean Meeus in Astronomical Algorithms
+
+  source: https://de.wikipedia.org/wiki/Spencers_Osterformel
+  source: https://en.wikipedia.org/wiki/Computus#Anonymous_Gregorian_algorithm
+  """
+  a = year % 19
+  b = year // 100
+  c = year % 100
+  d = b // 4
+  e = b % 4
+  f = (b + 8) // 25
+  g = (b - f + 1) // 3
+  h = (19 * a + b - d - g + 15) % 30
+  i = c // 4
+  k = c % 4
+  l = (32 + 2 * e + 2 * i - h - k) % 7
+  m = (a + 11 * h + 22 * l) // 451
+  n = (h + l - 7 * m + 114) // 31
+  o = (h + l - 7 * m + 114) % 31
+  return datetime.date(year, n, o + 1)
+
+# was not correct for 2020
 def gaußsche_osterformel(year):
   """Gaußsche Osterformel.
 
   :param year: the year to calculate the Easter Sunday
   :type year: int
-  
-  :returns: the day of Easter Sunday as a day in march.
-  :rtype: int
-  
+
+  :returns: the day of Easter Sunday (computed as a day in march).
+  :rtype: datetime.date
+
   :ivar X: Das Jahr / year
   :vartype X: int
   :ivar K(X): Die Säkularzahl
@@ -42,7 +84,7 @@ def gaußsche_osterformel(year):
   :vartype OE(OG,SZ): int
   :ivar OS(OG,OE): Das Datum des Ostersonntags als Märzdatum (32. März = 1. April usw.)
   :vartype OS(OG,OE): int
-  
+
   Algorithmus gilt für den Gregorianischen Kalender.
 
   source: https://de.wikipedia.org/wiki/Gau%C3%9Fsche_Osterformel
@@ -58,30 +100,29 @@ def gaußsche_osterformel(year):
   sz = 7 - (x + x // 4 + s) % 7
   oe = 7 - (og - sz) % 7
   os = og + oe
-  return os
+  
+  march = datetime.date(year, 3, 1)
+  day = march + datetime.timedelta(days=os)
+  return day
 
 def easter_sunday(year):
   """Easter Sunday.
 
   :param year: the year to calculate the Easter Sunday
   :type year: int
-  
+
   :returns: the day of Easter Sunday
   :rtype: datetime.date"""
-  import datetime
-  march = datetime.date(year, 3, 1)
-  day = march + datetime.timedelta(days=gaußsche_osterformel(year))
-  return day
+  return computus_anonymous_gregorian(year)
 
 def easter_friday(year):
   """Easter Friday.
 
   :param year: the year to calculate the Easter Friday
   :type year: int
-  
+
   :returns: the day of Easter Friday
   :rtype: datetime.date"""
-  import datetime
   day = easter_sunday(year) + datetime.timedelta(days=-2)
   return day
 
@@ -90,10 +131,9 @@ def easter_monday(year):
 
   :param year: the year to calculate the Easter Monday
   :type year: int
-  
+
   :returns: the day of Easter Monday
   :rtype: datetime.date"""
-  import datetime
   day = easter_sunday(year) + datetime.timedelta(days=+1)
   return day
 
@@ -102,10 +142,9 @@ def ascension_of_jesus(year):
 
   :param year: the year to calculate the ascension of Jesus
   :type year: int
-  
+
   :returns: the day of ascension of Jesus
   :rtype: datetime.date"""
-  import datetime
   day = easter_sunday(year) + datetime.timedelta(days=+39)
   return day
 
@@ -114,9 +153,8 @@ def pentecost(year):
 
   :param year: the year to calculate the Pentecost
   :type year: int
-  
+
   :returns: the day of Pentecost
   :rtype: datetime.date"""
-  import datetime
   day = easter_sunday(year) + datetime.timedelta(days=+49)
   return day