jpayne@68: # -*- coding: utf-8 -*-
jpayne@68: """
jpayne@68: This module offers a generic Easter computing method for any given year, using
jpayne@68: Western, Orthodox or Julian algorithms.
jpayne@68: """
jpayne@68: 
jpayne@68: import datetime
jpayne@68: 
jpayne@68: __all__ = ["easter", "EASTER_JULIAN", "EASTER_ORTHODOX", "EASTER_WESTERN"]
jpayne@68: 
jpayne@68: EASTER_JULIAN = 1
jpayne@68: EASTER_ORTHODOX = 2
jpayne@68: EASTER_WESTERN = 3
jpayne@68: 
jpayne@68: 
jpayne@68: def easter(year, method=EASTER_WESTERN):
jpayne@68:     """
jpayne@68:     This method was ported from the work done by GM Arts,
jpayne@68:     on top of the algorithm by Claus Tondering, which was
jpayne@68:     based in part on the algorithm of Ouding (1940), as
jpayne@68:     quoted in "Explanatory Supplement to the Astronomical
jpayne@68:     Almanac", P.  Kenneth Seidelmann, editor.
jpayne@68: 
jpayne@68:     This algorithm implements three different Easter
jpayne@68:     calculation methods:
jpayne@68: 
jpayne@68:     1. Original calculation in Julian calendar, valid in
jpayne@68:        dates after 326 AD
jpayne@68:     2. Original method, with date converted to Gregorian
jpayne@68:        calendar, valid in years 1583 to 4099
jpayne@68:     3. Revised method, in Gregorian calendar, valid in
jpayne@68:        years 1583 to 4099 as well
jpayne@68: 
jpayne@68:     These methods are represented by the constants:
jpayne@68: 
jpayne@68:     * ``EASTER_JULIAN   = 1``
jpayne@68:     * ``EASTER_ORTHODOX = 2``
jpayne@68:     * ``EASTER_WESTERN  = 3``
jpayne@68: 
jpayne@68:     The default method is method 3.
jpayne@68: 
jpayne@68:     More about the algorithm may be found at:
jpayne@68: 
jpayne@68:     `GM Arts: Easter Algorithms <http://www.gmarts.org/index.php?go=415>`_
jpayne@68: 
jpayne@68:     and
jpayne@68: 
jpayne@68:     `The Calendar FAQ: Easter <https://www.tondering.dk/claus/cal/easter.php>`_
jpayne@68: 
jpayne@68:     """
jpayne@68: 
jpayne@68:     if not (1 <= method <= 3):
jpayne@68:         raise ValueError("invalid method")
jpayne@68: 
jpayne@68:     # g - Golden year - 1
jpayne@68:     # c - Century
jpayne@68:     # h - (23 - Epact) mod 30
jpayne@68:     # i - Number of days from March 21 to Paschal Full Moon
jpayne@68:     # j - Weekday for PFM (0=Sunday, etc)
jpayne@68:     # p - Number of days from March 21 to Sunday on or before PFM
jpayne@68:     #     (-6 to 28 methods 1 & 3, to 56 for method 2)
jpayne@68:     # e - Extra days to add for method 2 (converting Julian
jpayne@68:     #     date to Gregorian date)
jpayne@68: 
jpayne@68:     y = year
jpayne@68:     g = y % 19
jpayne@68:     e = 0
jpayne@68:     if method < 3:
jpayne@68:         # Old method
jpayne@68:         i = (19*g + 15) % 30
jpayne@68:         j = (y + y//4 + i) % 7
jpayne@68:         if method == 2:
jpayne@68:             # Extra dates to convert Julian to Gregorian date
jpayne@68:             e = 10
jpayne@68:             if y > 1600:
jpayne@68:                 e = e + y//100 - 16 - (y//100 - 16)//4
jpayne@68:     else:
jpayne@68:         # New method
jpayne@68:         c = y//100
jpayne@68:         h = (c - c//4 - (8*c + 13)//25 + 19*g + 15) % 30
jpayne@68:         i = h - (h//28)*(1 - (h//28)*(29//(h + 1))*((21 - g)//11))
jpayne@68:         j = (y + y//4 + i + 2 - c + c//4) % 7
jpayne@68: 
jpayne@68:     # p can be from -6 to 56 corresponding to dates 22 March to 23 May
jpayne@68:     # (later dates apply to method 2, although 23 May never actually occurs)
jpayne@68:     p = i - j + e
jpayne@68:     d = 1 + (p + 27 + (p + 6)//40) % 31
jpayne@68:     m = 3 + (p + 26)//30
jpayne@68:     return datetime.date(int(y), int(m), int(d))