Module:Calendar

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local p = {}

-- Convert "Julian day number" (jdn) to a calendar date
-- "gregorian" is a 1 for gregorian calendar and 0 for Julian
-- based on https://en.wikipedia.org/wiki/Julian_day#Converting_Julian_or_Gregorian_calendar_date_to_Julian_day_number
function p._jdn2date(jdn, gregorian)
  local f, e, g, h, year, month, day

	f = jdn + 1401
	if gregorian>0 then
		 f = f + math.floor((math.floor((4*jdn + 274277) / 146097) * 3) / 4) - 38
	end
	e = 4*f + 3
	g = math.floor(math.fmod(e, 1461) / 4)
	h = 5*g + 2
	day   = math.floor(math.fmod (h,153) / 5) + 1
	month = math.fmod (math.floor(h/153) + 2, 12) + 1
	year  = math.floor(e/1461) - 4716 + math.floor((14 - month) / 12)
	
	-- If year is less than 1, subtract one to convert from a zero based date system to the
	-- common era system in which the year -1 (1 B.C.E) is followed by year 1 (1 C.E.).
	if year < 1 then
			year = year - 1
	end
	
	return string.format('%04i-%02i-%02i', year, month, day)
end

-- Convert calendar date to  "Julian day number" (jdn) 
-- "gregorian" is a 1 for gregorian calendar and 0 for Julian
-- based on  https://en.wikipedia.org/wiki/Julian_day#Converting_Julian_or_Gregorian_calendar_date_to_Julian_day_number
-- explanation based on http://www.cs.utsa.edu/~cs1063/projects/Spring2011/Project1/project1.html
function p._date2jdn(ISOdate, gregorian)
  
	year, month, day = ISOdate:match( "(-?%d%d%d%d)-(%d%d)-(%d%d)" )
	if not year then
		return nil
	elseif tonumber(year) < 0 then
		-- If year is less than 0, add one to convert from  the common era system in which
	    -- the year -1 (1 B.C.E) is followed by year 1 (1 C.E.) to a zero based date system
		year = year + 1
	end
	a = math.floor((14-month) / 12) -- will be 1 for January and February, and 0 for other months.
	y = year + 4800 - a             -- years since year –4800
	m = month + 12*a - 3            -- month number where 10 for January, 11 for February, 0 for March, 1 for April
	c = math.floor((153*m + 2)/5)   -- number of days since March 1
	if gregorian>0 then	
		b = math.floor(y/4) - math.floor(y/100) + math.floor(y/400) -- number of leap years since y==0 (year –4800)
		d = 32045                     -- offset so the result will be 0 for January 1, 4713 BCE
	else
		b = math.floor(y/4)           -- number of leap years since y==0 (year –4800)
	  d = 32083                     -- offset so the result will be 0 for January 1, 4713 BCE
	end
	return day + c + 365*y + b - d
end

-- Convert a date from Gregorian to Julian calendar
function p.Gregorian2Julian(frame)
	local JDN = p._date2jdn(frame.args[1], 1)
	if JDN then
		return p._jdn2date(JDN, 0)
	else
		return "Error parsing input date: " .. frame.args[1]
	end
end

-- Convert a date from Julian to Gregorian calendar
function p.Julian2Gregorian(frame)
	local JDN = p._date2jdn(frame.args[1], 0)
	if JDN then
		return p._jdn2date(JDN, 1)
	else
		return "Error parsing input date: " .. frame.args[1]
	end
end

-- Return day of week based on gregorian date. Mon->1, Tue->2, ..., Sun->7
function p.DayOfWeek(frame)
	local JDN = p._date2jdn(frame.args[1], 1)
	local day = math.fmod(JDN, 7) + 1
	if day then
		local LUT = { "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday" }
		return LUT[day]
	else
		return "Error parsing input date: " .. frame.args[1]
	end
end

return p