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