Module:Pâques
Le module est utilisé pour calculer la date de Pâques et dérivée de la date de dates de Pâques.
{{#invoke:Pâques|calcul|{{CURRENTYEAR}}}}
- 2025-04-20
{{#invoke:Pâques|calcul|{{CURRENTYEAR}}|methode=Orthodoxe}}
- 2025-04-20
{{#invoke:Pâques|calcul|{{CURRENTYEAR}}|format=j. F}}
- 2025-04-20
{{#invoke:Pâques|calcul|{{CURRENTYEAR}}|methode=Orthodoxe|format=j. F}}
- 20. avril
{{#invoke:Pâques|calcul|{{CURRENTYEAR}}|jour=Jeudi saint|format=j. F}}
- 17. avril
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 = -69, -- start of Niniveh lenten fast maximumOffset = 68, -- Feast of the Sacred Heart -- API apiEaster = "calcul", -- 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 = "jour", -- 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 = "Le parametre année requis est manquant", errorInvalidYear = "Declaration inexacte 'Annee': '%s'", errorInvalidOffset = "Declaration inexacte 'Jour': '%s'", errorInvalidMethod = "Declaration inexacte 'Methode': '%s'", errorYearOutOfRange = "Les dates de Paques ne peuvent être calcules que de 326 à 4099; Annee: %d", errorIncorrectMethod = "La Paques orthodoxe ou la occidentale depuis 1583; Annee: %d", errorUnknownMethod = "Methode de calcul inconnue: %d", methods = { ["Julian"] = 1, ["Julien"] = 1, -- alias for Julian ["Eastern"] = 2, ["Orthodoxe"] = 2, -- alias for Eastern ["Oriental"] = 2, -- alias for Eastern ["Western"] = 3, ["Romain"] = 3, -- alias for Roman ["Occidental"] = 3, -- alias for Roman }, relativeDates = { ["Septuagésime"] = -63, ["Sexagésime"] = -56, ["Jeudi gras"] = -52, ["Vendredi gras"] = -51, ["Carnaval"] = -51, ["Nelkensamstag"] = -50, ["Quinquagésime"] = -49, ["Dimanche gras"] = -49, ["Lundi des Roses"] = -48, ["Lundi gras"] = -48, ["Rosenmontag"] = -48, ["Mardi gras"] = -47, ["Carnaval"] = -47, ["Merci des cendres"] = -46, ["Invocabit"] = -42, ["Reminiscere"] = -35, ["Oculi"] = -28, ["Laetare"] = -21, ["Judica"] = -14, ["Dimanche de la Passion"] = -14, ["Dimanche des Rameaux"] = -7, ["Jeudi saint"] = -3, ["Vendredi saint"] = -2, ["Samedi saint"] = -1, ["Easter"] = 0, ["Pâques"] = 0, ["Lundi de Pâques"] = 1, ["Quasimodogeniti"] = 7, ["Quasimodo"] = 7, ["Schamm an-Nasim"] = 8, ["Misericordias Domini"] = 14, ["Jubilate"] = 21, ["Kantate"] = 28, ["Vocem jucunditatis"] = 35, ["Rogate"] = 35, ["Ascension Thursday"] = 39, ["Ascension"] = 39, ["Exaudi"] = 42, ["Pentecost"] = 49, ["Pentecôte"] = 49, ["Pfingsten"] = 50, ["Lundi de Pentecôte"] = 50, ["Corpus Christi"] = 60, ["Fête-Dieu"] = 60, ["Sacré-Cœur"] = 68, }, } 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 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, formatEeasteError(EasterData.errorUnknownMethod, method) end if d > 61 then -- when the oryginal calculation os 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