Module:Easter
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 date in the Julian calendar
["Eastern"] = 2, -- Eastern date in the Gregorian calendar
["Orthodox"] = 2, -- alias for Eastern
["Coptic"] = 2, -- alias for Eastern
["Ethiopian"] = 2, -- alias for Eastern
["Western"] = 3, -- Western date in the Gregorian calendar
["Gregorian"] = 3, -- alias for Western
["Catholic"] = 3, -- alias for Western
["Roman"] = 3, -- alias for Western
["Revised"] = 4, -- defacto alias for Western for now
["Meletian"] = 4, -- alias for Revised
["Astro"] = 5, -- defacto alias for Western for now
},
-- other proposed or reformed algorithms are not supported (yet):
--
-- * 4 "Meletian" = "Revised": Revised Julian Calendar from 1923 used by some Orthodox churches
-- with 900-year leap cycle, same as Gregorian until 2400 or so
-- * 5 "Astro": astronomically observed Nicean rule at the meridian of Jerusalem (Aleppo 1997 proposal),
-- differs from Gregorian sometimes
-- * 6 based on (equivalently) a range of valid dates in April:
-- * 61 "First": 1st Sunday in April = Sunday in 1–7 April
-- * 67 "Pepuzite": Sunday after 6 April = Sunday in 7–13 April
-- * 68 "April" = "Second": 2nd Sunday in April = Sunday in 8–14 April
-- * 69 "Fixed" = "UK": day after second Saturday in April = Sunday in 9–15 April
-- * 7 based on (equivalently) a range of valid days of the year (DOY):
-- * 75 "W14": Sunday of ISO week 14 = Sunday in 095–101
-- * 79 "Fifteen": 15th Sunday of the year: Sunday in 099–105
-- * 72 "W15": Sunday of ISO week 15 = Sunday in 102–108
-- * "Symmetry": Sym454/Sym010: Sunday of week 14 in a 293-year leap cycle
--
-- Breaking from the Biblical week cycle, any day of the week in the Gregorian calendar:
--
-- * "World": day 099, Sunday in the World Calendar
-- * "Positivist": day 098, Sunday in the Positivst Calendar
-- * "Quartodecimanism": Nisan 14 in the contemporary Jewish/Hebrew calendar, pre-Nicean
-- * "Quintodecimanism": Nisan 15 in the contemporary Jewish/Hebrew calendar, pre-Nicean
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,
["Invocabit Sunday"] = -42,
["Reminiscere Sunday"] = -35,
["Oculi Sunday"] = -28,
["Laetare Sunday"] = -21, -- Mothering Sunday
["Holy Week"] = -7,
["Palm Sunday"] = -7,
["Holy Monday"] = -6,
["Holy Tuesday"] = -5,
["Holy Wednesday"] = -4,
["Maundy Thursday"] = -3,
["Good Friday"] = -2, -- Crucifixion
["Holy Saturday"] = -1,
["Easter"] = 0, -- Easter Sunday, Resurrection
["Easter Monday"] = 1,
["Divine Mercy Sunday"] = 7,
["Misericordias Domini"] = 14,
["Jubilate Sunday"] = 21,
["Cantate Sunday"] = 28,
["Vocem jucunditatis"] = 35,
["Ascension Thursday"] = 39, -- Ascension
["Pentecost"] = 49, -- Whitsun
["Whit Monday"] = 50,
["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 "" .. message .. ""
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
4 = the revised calculation based on the
Meletian 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
if (year < 1600 or year > 2400) and method ~= 4 then
-- The Revised Julian Calendar is not really supported yet
return 0, formatEasterError(EasterData.errorYearOutOfRange, 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
-- Julian:
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
-- Eastern/Orthodox:
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
-- Gregorian:
elseif method == 3 or method == 4 then
-- calculate paschal full moon (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
-- when the original calculation is converted to the Gregorian calendar,
-- Easter Sunday can occur in May or even in June in the distant future
if d > 92 then
return 6, d - 92 -- June
elseif d > 61 then
return 5, d - 61 -- May
elseif d > 31 then
return 4, d - 31 -- April
else
return 3, d -- March
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