Module:Keppel date

Converts the current (or provided) date to a Keppel date. Used by Template:Keppel date.

Formula

\begin{aligned} y_\oplus &= \text{Earth year} \\ d_\oplus &= \text{Earth day of year (fractional)} \\ d_{\oplus_\text{max}}(y_\oplus) &= \begin{cases} 366 & (y_\oplus = 0 \pmod{4} \text{ and } y_\oplus \neq 0 \pmod{100}) \text{ or } y_\oplus = 0 \pmod{400} \\ 365 & \text{otherwise} \end{cases} \\ \text{offset}(y_\oplus) &= d_{\oplus_\text{max}}(y_\oplus) - 287 \\ d_{\text{K}_\text{max}}(y_\text{K}) &= \begin{cases} 391 & y_\text{K} = 65 \pmod{239} \text{ and } y_\text{K} = 2 \pmod{4} \\ 390 & y_\text{K} = 65 \pmod{239} \text{ or } y_\text{K} = 2 \pmod{4} \\ 389 & \text{otherwise} \end{cases} \\ y_\text{K}(y_\oplus) &= y_\oplus - 892 \\ y_\text{K} &= \begin{cases} y_\text{K}(y_\oplus) & d_\oplus - \text{offset}(y_\oplus) \geq \frac{d_{\oplus_\text{max}}(y_\oplus)}{d_{\text{K}_\text{max}}(y_\text{K}(y_\oplus))} \\ y_\text{K}(y_\oplus) - 1 & d_\oplus - \text{offset}(y_\oplus) < \frac{d_{\oplus_\text{max}}(y_\oplus)}{d_{\text{K}_\text{max}}(y_\text{K}(y_\oplus))} \end{cases} \\ d_\text{K} &= (\frac{d_\oplus - \text{offset}(y_\oplus)}{d_{\oplus_\text{max}}(y_\oplus)} \times d_{\text{K}_\text{max}}(y_\text{K}) - 1) \bmod{d_{\text{K}_\text{max}}(y_\text{K})} + 1 \\ L_\text{K} &= \lfloor \frac{d_\text{K} - 1}{32} \rfloor + 1 \\ d_{\text{K}_L} &= \lfloor (d_\text{K} - 1) \bmod{32} \rfloor + 1 \end{aligned}

---

local p = {}

-- libraries
local getArgs = require('Module:Arguments').getArgs
local yesno = require('Module:Yesno')

-- year calculations
local function isEarthLeapYear(year)
	-- every 4 years
	-- except for every 100 years
	-- except for every 400 years
	return (year % 400 == 0) or (year % 100 ~= 0 and year % 4 == 0)
end

local function getEarthYearLength(year)
	local yearLength = 365
	if isEarthLeapYear(year) then yearLength = yearLength + 1 end
	return yearLength
end

local function isLeapYear1(year)
	-- every 4 years (offset 2)
	return year % 4 == 2
end

local function isLeapYear2(year)
	-- every 239 years (offset 65)
	return year % 239 == 65
end

local function getYearLength(year)
	local yearLength = 389
	if isLeapYear1(year) then yearLength = yearLength + 1 end
	if isLeapYear2(year) then yearLength = yearLength + 1 end
	return yearLength
end

local function getYdayOffset(earthYear)
	local ydayOffset = 78
	if isEarthLeapYear(earthYear) then ydayOffset = ydayOffset + 1 end -- February 29
	return ydayOffset
end

-- lythryds
local lythryds = {
	'Liliyogh',
	'Avonslau',
	'Bovvilag',
	'Haelaidhe',
	'Gildorne',
	'Auvhlaus',
	'Ludervinn',
	'Glausonn',
	'Yahataidh',
	'Serelakkan',
	'Frosma',
	'Tegeirukk',
	'Intercal'
}

-- ochtdays
local ochtdays = {
	'Astresday',
	'Solsday',
	'Embresday',
	'Jadesday',
	'Ryvysday',
	'Tyrrhsday',
	'Lysisday',
	'Octresday'
}

-- https://amaranth-legacy.community/Seventeen_Suns
local sun_signs = {
	'[[File:Keppel-astrology-Alcaernon.png|32px|alt=]] Alcaernon',
	'[[File:Keppel-astrology-Eumrakh.png|32px|alt=]] Eumrakh',
	'[[File:Keppel-astrology-Aureolin.png|32px|alt=]] Aureolin',
	'[[File:Keppel-astrology-Pereptia.png|32px|alt=]] Pereptia',
	'[[File:Keppel-astrology-Sechmas.png|32px|alt=]] Sechmas',
	'[[File:Keppel-astrology-Mananakus.png|32px|alt=]] Mananakus',
	'[[File:Keppel-astrology-Luxor.png|32px|alt=]] Luxor',
	'[[File:Keppel-astrology-Illyre.png|32px|alt=]] Illyre',
	'[[File:Keppel-astrology-Glauryuz.png|32px|alt=]] Glauryuz',
	'[[File:Keppel-astrology-Schismata.png|32px|alt=]] Schismata',
	'[[File:Keppel-astrology-Annrava.png|32px|alt=]] Annrava',
	'[[File:Keppel-astrology-Yahasain.png|32px|alt=]] Yahasain',
	'[[File:Keppel-astrology-Regalion.png|32px|alt=]] Regalion',
	'[[File:Keppel-astrology-Vaalgrota.png|32px|alt=]] Vaalgrota',
	'[[File:Keppel-astrology-Cancrus.png|32px|alt=]] Cancrus',
	'[[File:Keppel-astrology-Eremoor.png|32px|alt=]] Eremoor',
	'[[File:Keppel-astrology-Haerox.png|32px|alt=]] Haerox'
}

-- date converter
function p.convert(time)
	-- get the current date
	local date = os.date('*t', time)
	-- add the time to yday
	date.yday = date.yday + (date.hour / 24) + (date.min / (24 * 60)) + (date.sec / (24 * 60 * 60))

	-- year is Earth year minus 892
	local year = date.year - 892
	local yearLength = getYearLength(year)

	-- if yday is before the start, it's the previous year
	local yday = date.yday - getYdayOffset(date.year)
	if yday < 1 then
		year = year - 1
		yearLength = getYearLength(year)
	end

	-- calculate the yday
	yday = yday / getEarthYearLength(date.year) * yearLength % yearLength

	-- if yday is before the start, it's an offset from the end of the previous year
	if yday < 1 then
		yday = yearLength + yday
	end

	-- a lythryd is 32 days
	local lythryd = math.floor((yday - 1) / 32) + 1

	-- to get the day of the lythryd, subtract the days in previous lythryds
	local day = math.floor(yday) - 32 * (lythryd - 1)

	-- get the time as well
	local ydayTime = select(2, math.modf(yday))
	local seconds = select(1, math.modf(ydayTime * 86400))
	local minutes = select(1, math.modf(seconds / 60))
	local hour = select(1, math.modf(minutes / 60))
	local minute = minutes % 60
	local second = seconds % 60

	return {
		year = year,
		yday = yday,
		lythryd = lythryd,
		day = day,
		hour = hour,
		minute = minute,
		second = second
	}
end

function p.invoke(frame)
	local args = getArgs(frame)
	local time
	if args['year'] and args['month'] and args['day'] then
		time = os.time{
			year = args['year'],
			month = args['month'],
			day = args['day'],
			hour = args['hour'] or 0,
			minute = args['minute'] or 0,
			second = args['second'] or 0
		}
	elseif args['time'] then
		time = args['time']
	elseif args[1] then
		time = args[1]
	else
		time = os.time()
	end

	return p.convert(time)
end

function p.main(frame)
	local args = getArgs(frame)

	local result = p.invoke(frame)
	local year
	if result.year <= 0 then
		year = (math.abs(result.year) + 1) .. ' AT'
	else
		year = result.year .. ' LE'
	end

	if yesno(args['year_only'] or false) then
		return year
	elseif yesno(args['month_day_only'] or false) then
		return string.format(
			'%s %d',
			lythryds[result.lythryd],
			result.day
		)
	else
		local formatted = string.format(
			'%s %d, %s',
			lythryds[result.lythryd],
			result.day,
			year
		)

		if yesno(args['show_ochtday'] or false) then
			formatted = string.format(
				'%s, %s',
				ochtdays[(result.day - 1) % 8 + 1],
				formatted
			)
		end

		if yesno(args['show_time'] or false) then
			formatted = string.format(
				'%s %02d:%02d:%02d',
				formatted,
				result.hour,
				result.minute,
				result.second
			)
		end

		if yesno(args['show_sun_sign'] or false) then
			formatted = string.format(
				'%s (%s)',
				formatted,
				sun_signs[math.floor(result.yday / 24) + 1]
			)
		end

		return formatted
	end
end

return p