1  # -*- coding: utf-8 -*-
   2  """
   3  This module offers a generic Easter computing method for any given year, using
   4  Western, Orthodox or Julian algorithms.
   5  """
   6  
   7  import datetime
   8  
   9  __all__ = ["easter", "EASTER_JULIAN", "EASTER_ORTHODOX", "EASTER_WESTERN"]
  10  
  11  EASTER_JULIAN = 1
  12  EASTER_ORTHODOX = 2
  13  EASTER_WESTERN = 3
  14  
  15  
  16  def easter(year, method=EASTER_WESTERN):
  17      """
  18      This method was ported from the work done by GM Arts,
  19      on top of the algorithm by Claus Tondering, which was
  20      based in part on the algorithm of Ouding (1940), as
  21      quoted in "Explanatory Supplement to the Astronomical
  22      Almanac", P.  Kenneth Seidelmann, editor.
  23  
  24      This algorithm implements three different Easter
  25      calculation methods:
  26  
  27      1. Original calculation in Julian calendar, valid in
  28         dates after 326 AD
  29      2. Original method, with date converted to Gregorian
  30         calendar, valid in years 1583 to 4099
  31      3. Revised method, in Gregorian calendar, valid in
  32         years 1583 to 4099 as well
  33  
  34      These methods are represented by the constants:
  35  
  36      * ``EASTER_JULIAN   = 1``
  37      * ``EASTER_ORTHODOX = 2``
  38      * ``EASTER_WESTERN  = 3``
  39  
  40      The default method is method 3.
  41  
  42      More about the algorithm may be found at:
  43  
  44      `GM Arts: Easter Algorithms <http://www.gmarts.org/index.php?go=415>`_
  45  
  46      and
  47  
  48      `The Calendar FAQ: Easter <https://www.tondering.dk/claus/cal/easter.php>`_
  49  
  50      """
  51  
  52      if not (1 <= method <= 3):
  53          raise ValueError("invalid method")
  54  
  55      # g - Golden year - 1
  56      # c - Century
  57      # h - (23 - Epact) mod 30
  58      # i - Number of days from March 21 to Paschal Full Moon
  59      # j - Weekday for PFM (0=Sunday, etc)
  60      # p - Number of days from March 21 to Sunday on or before PFM
  61      #     (-6 to 28 methods 1 & 3, to 56 for method 2)
  62      # e - Extra days to add for method 2 (converting Julian
  63      #     date to Gregorian date)
  64  
  65      y = year
  66      g = y % 19
  67      e = 0
  68      if method < 3:
  69          # Old method
  70          i = (19*g + 15) % 30
  71          j = (y + y//4 + i) % 7
  72          if method == 2:
  73              # Extra dates to convert Julian to Gregorian date
  74              e = 10
  75              if y > 1600:
  76                  e = e + y//100 - 16 - (y//100 - 16)//4
  77      else:
  78          # New method
  79          c = y//100
  80          h = (c - c//4 - (8*c + 13)//25 + 19*g + 15) % 30
  81          i = h - (h//28)*(1 - (h//28)*(29//(h + 1))*((21 - g)//11))
  82          j = (y + y//4 + i + 2 - c + c//4) % 7
  83  
  84      # p can be from -6 to 56 corresponding to dates 22 March to 23 May
  85      # (later dates apply to method 2, although 23 May never actually occurs)
  86      p = i - j + e
  87      d = 1 + (p + 27 + (p + 6)//40) % 31
  88      m = 3 + (p + 26)//30
  89      return datetime.date(int(y), int(m), int(d))
  90