Module:Pasen
Module om de paasdatum en daarvan afgeleide data te berekenen.
Bereken
Functie om de datum van Pasen of van een aan Pasen gerelateerde feestdag te berekenen.
parameters
| Veld | Doel | Voorbeeldparameter |
|---|---|---|
| 1 | Jaar | 2024 of 1882
|
| methode | Berekeningsmethode van de paasdatum:
|
Oosters om de paasdatum te berekenen in de Orthodoxe ritus.
|
| dag | Naam van de aan Pasen gerelateerde feestdag, of een geheel aantal dagen voor (negatief) of na (positief) Paaszondag. De volgende dagen zijn bij naam beschikbaar:
|
49 of met hetzelfde resultaat: Pinksteren
|
| formaat | Beschrijft het datumformaat voor de uitvoer, op dezelfde manier als voor de #time-parseerfunctie. Verstekformaat is Y-m-d. Er is een speciale waarde geen die formattering uitschakelt.
|
j xd
|
voorbeelden
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}}}- 2024-03-31
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}|methode=Oosters}}- 2024-05-05
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}|formaat=[[j xg]]}}- 31 maart
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}|methode=Oosters|formaat=[[j xg]]}}- 5 mei
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}|dag=Aswoensdag}}- 2024-02-14
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}|methode=Oosters|dag=Aswoensdag}}- 2024-03-20
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}|formaat=[[j xg]] (l)|dag=Aswoensdag}}- 14 februari (woensdag)
{{#invoke:Pasen|Bereken|{{CURRENTYEAR}}|methode=Oosters|formaat=[[j xg]] (l)|dag=Aswoensdag}}- 20 maart (woensdag)
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 = "geen", -- prevent from final date formatting
defaultOffset = 0, -- the Easter date
minimumOffset = -63, -- Septuagesima
maximumOffset = 252, -- 27e zondag na Trinitatis
-- API
apiEaster = "Bereken", -- public function name
argEasterYear = 1, -- index or name of the argument with year
argEasterMethod = "methode", -- index or name of the argument with calculation method
argEasterOffset = "dag", -- index or name of the argument with offset in days relative to the calculated Easter Sunday
argEasterFormat = "formaat", -- index or name of the argument with date output format (#time style)
-- errors
errorMissingYear = "Ontbrekende verplichte parameter 1 (jaar)",
errorInvalidYear = "Incorrecte parameter 1 (jaar): '%s'",
errorInvalidOffset = "Incorrecte parameter 'dag': '%s'",
errorInvalidMethod = "Incorrecte parameter 'methode': '%s'",
errorYearOutOfRange = "Paasdata zijn beschikbaar tussen de jaren 326 en 4099; jaar: %d",
errorIncorrectMethod = "Westers of Orthodox Pasen bestaan sinds 1583; jaar: %d",
errorUnknownMethod = "Onbekende methode: %d",
methods = {
["Juliaans"] = 1,
["Oosters"] = 2,
["Orthodox"] = 2, -- alias voor Oosters
["Koptisch"] = 2, -- alias voor Oosters
["Ethiopisch"] = 2, -- alias voor Oosters
["Westers"] = 3,
["Gregoriaans"] = 3, -- alias voor Westers
["Rooms"] = 3, -- alias voor Westers
},
-- 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,
["Quinquagesima"] = -49,
["Estomihi"] = -49,
["Vastenavond"] = -47,
["Carnaval"] = -47,
["Aswoensdag"] = -46,
["Invocabit"] = -42,
["Reminiscere"] = -35,
["Oculi"] = -28,
["Laetare"] = -21,
["Halfvasten"] = -21,
["Judica"] = -14,
["Palmpasen"] = -7,
["Schorselwoensdag"] = -4,
["Schortelwoensdag"] = -4,
["Witte Donderdag"] = -3,
["Goede Vrijdag"] = -2,
["Stille Zaterdag"] = -1,
["Pasen"] = 0,
["Paasmaandag"] = 1,
["Tweede paasdag"] = 1,
["Beloken Pasen"] = 7,
["Quasimodo-zondag"] = 7,
["Quasi modo geniti"] = 7,
["Misericordias Domini"] = 14,
["Jubilate"] = 21,
["Cantate"] = 28,
["Rogate"] = 35,
["Hemelvaart"] = 39,
["Exaudi"] = 42,
["Wezenzondag"] = 42,
["Pinksteren"] = 49,
["Pinkstermaandag"] = 50,
["Trinitatis"] = 56,
["Sacramentsdag"] = 60,
["Sacramentszondag"] = 63,
["1e zondag na Trinitatis"] = 63,
["Heilig Hart"] = 68,
["Onbevlekt Hart van Maria"] = 69,
["2e zondag na Trinitatis"] = 70,
["3e zondag na Trinitatis"] = 77,
["4e zondag na Trinitatis"] = 84,
["5e zondag na Trinitatis"] = 91,
["6e zondag na Trinitatis"] = 98,
["7e zondag na Trinitatis"] = 105,
["8e zondag na Trinitatis"] = 112,
["9e zondag na Trinitatis"] = 119,
["10e zondag na Trinitatis"] = 126,
["11e zondag na Trinitatis"] = 133,
["12e zondag na Trinitatis"] = 140,
["13e zondag na Trinitatis"] = 147,
["14e zondag na Trinitatis"] = 154,
["15e zondag na Trinitatis"] = 161,
["16e zondag na Trinitatis"] = 168,
["17e zondag na Trinitatis"] = 175,
["18e zondag na Trinitatis"] = 182,
["19e zondag na Trinitatis"] = 189,
["20e zondag na Trinitatis"] = 196,
["21e zondag na Trinitatis"] = 203,
["22e zondag na Trinitatis"] = 210,
["23e zondag na Trinitatis"] = 217,
["24e zondag na Trinitatis"] = 224, -- bestaat niet in elk kerkelijk jaar
["25e zondag na Trinitatis"] = 231, -- bestaat niet in elk kerkelijk jaar
["26e zondag na Trinitatis"] = 238, -- bestaat niet in elk kerkelijk jaar
["27e zondag na Trinitatis"] = 245, -- bestaat niet in elk kerkelijk jaar
["28e zondag na Trinitatis"] = 252, -- bestaat niet in elk kerkelijk jaar
},
}
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