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

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