Module:Easter
Revision as of 22:04, 8 July 2016 by en>Crissov (some minor fixes, comments, named aliases)
Module to calculate Easter dates and dates relative to Easter.
Calculate
Function to calculate Easter date or date of the event related to Easter.
arguments
| Field | Purpose | Example argument |
|---|---|---|
| 1 | Year | 2024 or 1882
|
| method | Calculation method of the Easter date:
|
Eastern to calculate Easter date in the Orthodox rite.
|
| day | Name of the event related to Easter date or integer number of days before (negative) or after (positive) Easter Sunday. The following days are available by name:
|
49 or interchangeably Pentecost
|
| format | Describes date format in the final output, which is the same as used in #time parser function. Default format is Y-m-d. There is a special value none that prevents from final date formatting.
|
j xd
|
examples
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}}}- 2024-03-31
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}|method=Eastern}}- 2024-05-05
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}|format=[[j xg]]}}- 31 March
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}|method=Eastern|format=[[j xg]]}}- 5 May
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}|day=Ash Wednesday}}- 2024-02-14
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}|method=Eastern|day=Ash Wednesday}}- 2024-03-20
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}|format=[[j xg]] (l)|day=Ash Wednesday}}- 14 February (Wednesday)
{{#invoke:Easter|Calculate|{{CURRENTYEAR}}|method=Eastern|format=[[j xg]] (l)|day=Ash Wednesday}}- 20 March (Wednesday)
local m = {}
local EasterData = {
defaultMethod = 3, -- default method of Easter date calculation when Easter type is not given
defaultFormat = "Y-m-d", -- default date output format
noFormat = "none", -- prevent from final date formatting
defaultOffset = 0, -- the Easter date
minimumOffset = -63, -- Septuagesima
maximumOffset = 69, -- Feast of the Immaculate Heart of Mary
-- API
apiEaster = "Calculate", -- public function name
argEasterYear = 1, -- index or name of the argument with year
argEasterMethod = "method", -- index or name of the argument with calculation method
argEasterOffset = "day", -- index or name of the argument with offset in days relative to the calculated Easter Sunday
argEasterFormat = "format", -- index or name of the argument with date output format (#time style)
-- errors
errorMissingYear = "Missing mandatory argument 'year'",
errorInvalidYear = "Incorrect argument 'year': '%s'",
errorInvalidOffset = "Incorrect argument 'day': '%s'",
errorInvalidMethod = "Incorrect argument 'method': '%s'",
errorYearOutOfRange = "Easter dates are available between years 326 and 4099; year: %d",
errorIncorrectMethod = "Western or Orthodox Easter exists since 1583; year: %d",
errorUnknownMethod = "Unknown method: %d",
methods = {
["Julian"] = 1,
["Eastern"] = 2,
["Orthodox"] = 2, -- alias for Eastern
["Coptic"] = 2, -- alias for Eastern
["Ethiopian"] = 2, -- alias for Eastern
["Western"] = 3,
["Gregorian"] = 3, -- alias for Western
["Roman"] = 3, -- alias for Western
},
-- the Meletian/Revised Julian Calendar from 1923 used by some Orthodox churches
-- and any proposed reformed algorithms are not supported (yet):
-- * astronomically observed Nicean rule at the meridian of Jerusalem (Aleppo 1997 proposal), differs from Gregorian in
-- * fifteenth Sunday of the year: Sunday in 099–105 day of the year
-- * Sunday after second Saturday in April (UK): Sunday in 9–15 April
-- * second Sunday in April: Sunday in 8–14 April
-- * Sunday after 6 April (Pepuzite sect): Sunday in 7–13 April
-- * World Calendar: day 099, any day of the week in Gregorian/Julian calendar
-- * Positivist Calendar: day 098, any day of the week in Gregorian/Julian calendar
-- * Sunday of ISO week 14: Sunday in 099–105 day of the year
-- * Sunday of ISO week 15: Sunday in 106–112 day of the year
-- * Nisan 14: any day of the week
-- * Nisan 15: any day of the week
relativeDates = {
["Septuagesima"] = -63,
["Sexagesima"] = -56,
["Fat Thursday"] = -52,
["Quinquagesima"] = -49, -- Estomihi, Shrove Sunday
["Shrove Monday"] = -48, -- Rose Monday
["Shrove Tuesday"] = -47, -- Mardi Gras, Carnival
["Ash Wednesday"] = -46,
["Laetare Sunday"] = -21,
["Palm Sunday"] = -7,
["Holy Wednesday"] = -4,
["Maundy Thursday"] = -3,
["Good Friday"] = -2, -- Crucifixion
["Holy Saturday"] = -1,
["Easter"] = 0, -- Easter Sunday, Resurrection
["Easter Monday"] = 1,
["Divine Mercy"] = 7,
["Ascension Thursday"] = 39, -- Ascension
["Pentecost"] = 49, -- Whitsun
["Trinity Sunday"] = 56,
["Corpus Christi"] = 60, -- Body and Blood of Christ
["Sacred Heart"] = 68,
["Immaculate Heart"] = 69,
},
}
local function formatEasterError(message, ...)
if select('#', ... ) > 0 then
message = string.format(message, ...)
end
return "<span class=\"error\">" .. message .. "</span>"
end
local function loadEasterYear(year)
if not year then
return false, formatEasterError(EasterData.errorMissingYear)
end
local result = tonumber(year)
if not result or math.floor(result) ~= result then
return false, formatEasterError(EasterData.errorInvalidYear, year)
end
return true, result
end
local function loadEasterMethod(method, year)
local result = EasterData.defaultMethod
if method then
result = EasterData.methods[method]
if not result then
return false, formatEasterError(EasterData.errorInvalidMethod, method)
end
end
if year < 1583 then
result = 1
end
return true, result
end
local function loadEasterOffset(day)
if not day then
return true, ""
end
local data = EasterData.relativeDates
local offset = tonumber(day)
if not offset then
offset = data[day]
end
if not offset or offset ~= math.floor(offset) or offset < EasterData.minimumOffset or offset > EasterData.maximumOffset then
return false, formatEasterError(EasterData.errorInvalidOffset, day)
end
if offset < -1 then
return true, string.format(" %d days", offset)
elseif offset == -1 then
return true, " -1 day"
elseif offset == 0 then
return true, ""
elseif offset == 1 then
return true, " +1 day"
else -- if offset > 1 then
return true, string.format(" +%d days", offset)
end
end
local function loadEasterFormat(fmt)
if fmt == EasterData.noFormat then
return true, nil
elseif not fmt then
return true, EasterData.defaultFormat
else
return true, fmt
end
end
--[[
PURPOSE: This function returns Easter Sunday day and month
for a specified year and method.
INPUTS: Year - Any year between 326 and 4099.
Method - 1 = the original calculation based on the
Julian calendar
2 = the original calculation, with the
Julian date converted to the
equivalent Gregorian calendar
3 = the revised calculation based on the
Gregorian calendar
OUTPUTS: None.
RETURNS: 0, error message - Error; invalid arguments
month, day - month and day of the Sunday
NOTES:
The code is translated from DN OSP 6.4.0 sources.
The roots of the code might be found in
http://www.gmarts.org/index.php?go=415
ORIGINAL NOTES:
This algorithm is an arithmetic interpretation
of the 3 step Easter Dating Method developed
by Ron Mallen 1985, as a vast improvement on
the method described in the Common Prayer Book
Published Australian Almanac 1988
Refer to this publication, or the Canberra Library
for a clear understanding of the method used
Because this algorithm is a direct translation of
the official tables, it can be easily proved to be
100% correct
It's free! Please do not modify code or comments!
]]
local function calculateEasterDate(year, method)
if year < 326 or year > 4099 then
-- Easter dates are valid for years between 326 and 4099
-- Method 2 would have to support dates in June thereafter
return 0, formatEasterError(EasterData.errorYearOutOfRange, year)
end
if year < 1583 and method ~= 1 then
-- Western or Orthodox Easter is valid since 1583
return 0, formatEasterError(EasterData.errorIncorrectMethod, year)
end
-- intermediate result
local firstDig = math.floor(year / 100)
local remain19 = year % 19
local temp = 0
-- table A to E results
local tA = 0
local tB = 0
local tC = 0
local tD = 0
local tE = 0
-- Easter Sunday day
local d = 0
if method == 1 or method == 2 then
-- calculate PFM date
tA = ((225 - 11 * remain19) % 30) + 21
-- find the next Sunday
tB = (tA - 19) % 7
tC = (40 - firstDig) % 7
temp = year % 100
tD = (temp + math.floor(temp / 4)) % 7
tE = ((20 - tB - tC - tD) % 7) + 1
d = tA + tE
if method == 2 then
-- convert Julian to Gregorian date
-- 10 days were skipped in the Gregorian calendar from 5-14 Oct 1582
temp = 10
-- only 1 in every 4 century years are leap years in the Gregorian
-- calendar (every century is a leap year in the Julian calendar)
if year > 1600 then
temp = temp + firstDig - 16 - math.floor((firstDig - 16) / 4)
end
d = d + temp
end
elseif method == 3 then
-- calculate PFM date
temp = math.floor((firstDig - 15) / 2) + 202 - 11 * remain19
if firstDig > 26 then
temp = temp - 1
end
if firstDig > 38 then
temp = temp - 1
end
if firstDig == 21 or firstDig == 24 or firstDig == 25 or firstDig == 33 or firstDig == 36 or firstDig == 37 then
temp = temp - 1
end
temp = temp % 30
tA = temp + 21
if temp == 29 then
tA = tA - 1
end
if temp == 28 and remain19 > 10 then
tA = tA - 1
end
-- find the next Sunday
tB = (tA - 19) % 7
tC = (40 - firstDig) % 4
if tC == 3 then
tC = tC + 1
end
if tC > 1 then
tC = tC + 1
end
temp = year % 100
tD = (temp + math.floor(temp / 4)) % 7
tE = ((20 - tB - tC - tD) % 7) + 1
d = tA + tE
else
-- Unknown method
return 0, formatEasterError(EasterData.errorUnknownMethod, method)
end
if d > 61 then
-- when the original calculation is converted to the Gregorian
-- calendar, Easter Sunday can occur in May
return 5, d - 61
elseif d > 31 then
return 4, d - 31
else
return 3, d
end
end
local function Easter(args)
local ok
local year
ok, year = loadEasterYear(args[EasterData.argEasterYear])
if not ok then
return year
end
local method
ok, method = loadEasterMethod(args[EasterData.argEasterMethod], year)
if not ok then
return method
end
local offset
ok, offset = loadEasterOffset(args[EasterData.argEasterOffset])
if not ok then
return offset
end
local format
ok, format = loadEasterFormat(args[EasterData.argEasterFormat])
if not ok then
return format
end
local month, day = calculateEasterDate(year, method)
if month == 0 then
return day
end
local result = string.format("%04d-%02d-%02d%s", year, month, day, offset)
if format then
result = mw.language.getContentLanguage():formatDate(format, result)
end
return result
end
m[EasterData.apiEaster] = function (frame)
return Easter(frame.args)
end
return m
