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Module:Easter

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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 "<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
                       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
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