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 = {}

-- leap year checks
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 isKeppelLeapYear1(year)
	-- every 4 years beginning on year 2
	return year % 4 == 2 
end

local function isKeppelLeapYear2(year)
	-- every 239 years beginning on year 65
	return year % 239 == 65
end

-- lythryd number to name map
local lythryd = {
	'Liliyogh',
	'Avonslau',
	'Bovvilag',
	'Haelaidhe',
	'Gildorne',
	'Glausonn',
	'Ludervinn',
	'Auvhlaus',
	'Yahataidh',
	'Serelakkan',
	'Frosma',
	'Tegeirukk',
	'Intercal'
}

function p.convertDate(date)
	-- maximum amount of days in a year (Earth)
	local ydayMaxEarth = isEarthLeapYear(date.year) and 366 or 365
	-- maximum amount of days in a year (Keppel)
	local ydayMax = 389
	if isEarthLeapYear(date.year) then ydayMax = ydayMax + 1 end
	if isKeppelLeapYear1(date.year) then ydayMax = ydayMax + 1 end
	if isKeppelLeapYear2(date.year) then ydayMax = ydayMax + 1 end
	-- rollover offset
	local rolloverOffset = isEarthLeapYear(date.year) and 80 or 79

	-- Keppel year and yday
	local year = date.year - 892
	local yday = ((ydayMax * (date.yday - rolloverOffset)) / ydayMaxEarth) % ydayMax
	local daynumraw = math.floor(yday)

	-- lythryd
	local lythrydNumber = math.ceil(yday / 32)
	local lythrydDay = math.ceil((yday - lythrydNumber * 32) % 32)

	return {
		year = year,
		daynumraw = daynumraw,
		lythrydNumber = lythrydNumber,
		lythryd = lythryd[lythrydNumber],
		lythrydDay = lythrydDay
	}
end

function p.main(frame)
	local args = require('Module:Arguments').getArgs(frame)

	local time = args['time'] or os.time()
	local date = os.date('!*t', time)
	local result = p.convertDate(date)

	return result.lythryd .. ' ' .. result.lythrydDay .. ', ' .. result.year .. ' (yday ' .. result.daynumraw .. ')'
end

return p