Module:Date/மணல்தொட்டி
-- Date functions for use by other modules.
 -- I18N and time zones are not supported.
 
 local MINUS = '−'  -- Unicode U+2212 MINUS SIGN
 local floor = math.floor
 
 local Date, DateDiff, diffmt  -- forward declarations
 local uniq = { 'unique identifier' }
 
 local function is_date(t)
 	-- The system used to make a date read-only means there is no unique
 	-- metatable that is conveniently accessible to check.
 	return type(t) == 'table' and t._id == uniq
 end
 
 local function is_diff(t)
 	return type(t) == 'table' and getmetatable(t) == diffmt
 end
 
 local function _list_join(list, sep)
 	return table.concat(list, sep)
 end
 
 local function collection()
 	-- Return a table to hold items.
 	return {
 		n = 0,
 		add = function (self, item)
 			self.n = self.n + 1
 			self[self.n] = item
 		end,
 		join = _list_join,
 	}
 end
 
 local function strip_to_nil(text)
 	-- If text is a string, return its trimmed content, or nil if empty.
 	-- Otherwise return text (convenient when Date fields are provided from
 	-- another module which may pass a string, a number, or another type).
 	if type(text) == 'string' then
 		text = text:match('(%S.-)%s*$')
 	end
 	return text
 end
 
 local function is_leap_year(year, calname)
 	-- Return true if year is a leap year.
 	if calname == 'Julian' then
 		return year % 4 == 0
 	end
 	return (year % 4 == 0 and year % 100 ~= 0) or year % 400 == 0
 end
 
 local function days_in_month(year, month, calname)
 	-- Return number of days (1..31) in given month (1..12).
 	if month == 2 and is_leap_year(year, calname) then
 		return 29
 	end
 	return ({ 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 })[month]
 end
 
 local function h_m_s(time)
 	-- Return hour, minute, second extracted from fraction of a day.
 	time = floor(time * 24 * 3600 + 0.5)  -- number of seconds
 	local second = time % 60
 	time = floor(time / 60)
 	return floor(time / 60), time % 60, second
 end
 
 local function hms(date)
 	-- Return fraction of a day from date's time, where (0 &lt;= fraction &lt; 1)
 	-- if the values are valid, but could be anything if outside range.
 	return (date.hour + (date.minute + date.second / 60) / 60) / 24
 end
 
 local function julian_date(date)
 	-- Return jd, jdz from a Julian or Gregorian calendar date where
 	--   jd = Julian date and its fractional part is zero at noon
 	--   jdz = same, but assume time is 00:00:00 if no time given
 	-- http://www.tondering.dk/claus/cal/julperiod.php#formula
 	-- Testing shows this works for all dates from year -9999 to 9999!
 	-- JDN 0 is the 24-hour period starting at noon UTC on Monday
 	--    1 January 4713 BC  = (-4712, 1, 1)   Julian calendar
 	--   24 November 4714 BC = (-4713, 11, 24) Gregorian calendar
 	local offset
 	local a = floor((14 - date.month)/12)
 	local y = date.year + 4800 - a
 	if date.calendar == 'Julian' then
 		offset = floor(y/4) - 32083
 	else
 		offset = floor(y/4) - floor(y/100) + floor(y/400) - 32045
 	end
 	local m = date.month + 12*a - 3
 	local jd = date.day + floor((153*m + 2)/5) + 365*y + offset
 	if date.hastime then
 		jd = jd + hms(date) - 0.5
 		return jd, jd
 	end
 	return jd, jd - 0.5
 end
 
 local function set_date_from_jd(date)
 	-- Set the fields of table date from its Julian date field.
 	-- Return true if date is valid.
 	-- http://www.tondering.dk/claus/cal/julperiod.php#formula
 	-- This handles the proleptic Julian and Gregorian calendars.
 	-- Negative Julian dates are not defined but they work.
 	local calname = date.calendar
 	local low, high  -- min/max limits for date ranges −9999-01-01 to 9999-12-31
 	if calname == 'Gregorian' then
 		low, high = -1930999.5, 5373484.49999
 	elseif calname == 'Julian' then
 		low, high = -1931076.5, 5373557.49999
 	else
 		return
 	end
 	local jd = date.jd
 	if not (type(jd) == 'number' and low &lt;= jd and jd &lt;= high) then
 		return
 	end
 	local jdn = floor(jd)
 	if date.hastime then
 		local time = jd - jdn  -- 0 &lt;= time &lt; 1
 		if time &gt;= 0.5 then    -- if at or after midnight of next day
 			jdn = jdn + 1
 			time = time - 0.5
 		else
 			time = time + 0.5
 		end
 		date.hour, date.minute, date.second = h_m_s(time)
 	else
 		date.second = 0
 		date.minute = 0
 		date.hour = 0
 	end
 	local b, c
 	if calname == 'Julian' then
 		b = 0
 		c = jdn + 32082
 	else  -- Gregorian
 		local a = jdn + 32044
 		b = floor((4*a + 3)/146097)
 		c = a - floor(146097*b/4)
 	end
 	local d = floor((4*c + 3)/1461)
 	local e = c - floor(1461*d/4)
 	local m = floor((5*e + 2)/153)
 	date.day = e - floor((153*m + 2)/5) + 1
 	date.month = m + 3 - 12*floor(m/10)
 	date.year = 100*b + d - 4800 + floor(m/10)
 	return true
 end
 
 local function fix_numbers(numbers, y, m, d, H, M, S, partial, hastime, calendar)
 	-- Put the result of normalizing the given values in table numbers.
 	-- The result will have valid m, d values if y is valid; caller checks y.
 	-- The logic of PHP mktime is followed where m or d can be zero to mean
 	-- the previous unit, and -1 is the one before that, etc.
 	-- Positive values carry forward.
 	local date
 	if not (1 &lt;= m and m &lt;= 12) then
 		date = Date(y, 1, 1)
 		if not date then return end
 		date = date + ((m - 1) .. 'm')
 		y, m = date.year, date.month
 	end
 	local days_hms
 	if not partial then
 		if hastime and H and M and S then
 			if not (0 &lt;= H and H &lt;= 23 and
 					0 &lt;= M and M &lt;= 59 and
 					0 &lt;= S and S &lt;= 59) then
 				days_hms = hms({ hour = H, minute = M, second = S })
 			end
 		end
 		if days_hms or not (1 &lt;= d and d &lt;= days_in_month(y, m, calendar)) then
 			date = date or Date(y, m, 1)
 			if not date then return end
 			date = date + (d - 1 + (days_hms or 0))
 			y, m, d = date.year, date.month, date.day
 			if days_hms then
 				H, M, S = date.hour, date.minute, date.second
 			end
 		end
 	end
 	numbers.year = y
 	numbers.month = m
 	numbers.day = d
 	if days_hms then
 		-- Don't set H unless it was valid because a valid H will set hastime.
 		numbers.hour = H
 		numbers.minute = M
 		numbers.second = S
 	end
 end
 
 local function set_date_from_numbers(date, numbers, options)
 	-- Set the fields of table date from numeric values.
 	-- Return true if date is valid.
 	if type(numbers) ~= 'table' then
 		return
 	end
 	local y = numbers.year   or date.year
 	local m = numbers.month  or date.month
 	local d = numbers.day    or date.day
 	local H = numbers.hour
 	local M = numbers.minute or date.minute or 0
 	local S = numbers.second or date.second or 0
 	local need_fix
 	if y and m and d then
 		date.partial = nil
 		if not (-9999 &lt;= y and y &lt;= 9999 and
 			1 &lt;= m and m &lt;= 12 and
 			1 &lt;= d and d &lt;= days_in_month(y, m, date.calendar)) then
 				if not date.want_fix then
 					return
 				end
 				need_fix = true
 		end
 	elseif y and date.partial then
 		if d or not (-9999 &lt;= y and y &lt;= 9999) then
 			return
 		end
 		if m and not (1 &lt;= m and m &lt;= 12) then
 			if not date.want_fix then
 				return
 			end
 			need_fix = true
 		end
 	else
 		return
 	end
 	if date.partial then
 		H = nil  -- ignore any time
 		M = nil
 		S = nil
 	else
 		if H then
 			-- It is not possible to set M or S without also setting H.
 			date.hastime = true
 		else
 			H = 0
 		end
 		if not (0 &lt;= H and H &lt;= 23 and
 				0 &lt;= M and M &lt;= 59 and
 				0 &lt;= S and S &lt;= 59) then
 			if date.want_fix then
 				need_fix = true
 			else
 				return
 			end
 		end
 	end
 	date.want_fix = nil
 	if need_fix then
 		fix_numbers(numbers, y, m, d, H, M, S, date.partial, date.hastime, date.calendar)
 		return set_date_from_numbers(date, numbers, options)
 	end
 	date.year = y    -- -9999 to 9999 ('n BC' → year = 1 - n)
 	date.month = m   -- 1 to 12 (may be nil if partial)
 	date.day = d     -- 1 to 31 (* = nil if partial)
 	date.hour = H    -- 0 to 59 (*)
 	date.minute = M  -- 0 to 59 (*)
 	date.second = S  -- 0 to 59 (*)
 	if type(options) == 'table' then
 		for _, k in ipairs({ 'am', 'era', 'format' }) do
 			if options[k] then
 				date.options[k] = options[k]
 			end
 		end
 	end
 	return true
 end
 
 local function make_option_table(options1, options2)
 	-- If options1 is a string, return a table with its settings, or
 	-- if it is a table, use its settings.
 	-- Missing options are set from table options2 or defaults.
 	-- If a default is used, a flag is set so caller knows the value was not intentionally set.
 	-- Valid option settings are:
 	-- am: 'am', 'a.m.', 'AM', 'A.M.'
 	--     'pm', 'p.m.', 'PM', 'P.M.' (each has same meaning as corresponding item above)
 	-- era: 'BCMINUS', 'BCNEGATIVE', 'BC', 'B.C.', 'BCE', 'B.C.E.', 'AD', 'A.D.', 'CE', 'C.E.'
 	-- Option am = 'am' does not mean the hour is AM; it means 'am' or 'pm' is used, depending on the hour,
 	--    and am = 'pm' has the same meaning.
 	-- Similarly, era = 'BC' means 'BC' is used if year &lt;= 0.
 	-- BCMINUS displays a MINUS if year &lt; 0 and the display format does not include %{era}.
 	-- BCNEGATIVE is similar but displays a hyphen.
 	local result = { bydefault = {} }
 	if type(options1) == 'table' then
 		result.am = options1.am
 		result.era = options1.era
 	elseif type(options1) == 'string' then
 		-- Example: 'am:AM era:BC' or 'am=AM era=BC'.
 		for item in options1:gmatch('%S+') do
 			local lhs, rhs = item:match('^(%w+)[:=](.+)$')
 			if lhs then
 				result[lhs] = rhs
 			end
 		end
 	end
 	options2 = type(options2) == 'table' and options2 or {}
 	local defaults = { am = 'am', era = 'BC' }
 	for k, v in pairs(defaults) do
 		if not result[k] then
 			if options2[k] then
 				result[k] = options2[k]
 			else
 				result[k] = v
 				result.bydefault[k] = true
 			end
 		end
 	end
 	return result
 end
 
 local ampm_options = {
 	-- lhs = input text accepted as an am/pm option
 	-- rhs = code used internally
 	['am']   = 'am',
 	['AM']   = 'AM',
 	['a.m.'] = 'a.m.',
 	['A.M.'] = 'A.M.',
 	['pm']   = 'am',  -- same as am
 	['PM']   = 'AM',
 	['p.m.'] = 'a.m.',
 	['P.M.'] = 'A.M.',
 }
 
 local era_text = {
 	-- Text for displaying an era with a positive year (after adjusting
 	-- by replacing year with 1 - year if date.year &lt;= 0).
 	-- options.era = { year&lt;=0 , year&gt;0 }
 	['BCMINUS']    = { 'BC'    , ''    , isbc = true, sign = MINUS },
 	['BCNEGATIVE'] = { 'BC'    , ''    , isbc = true, sign = '-'   },
 	['BC']         = { 'BC'    , ''    , isbc = true },
 	['B.C.']       = { 'B.C.'  , ''    , isbc = true },
 	['BCE']        = { 'BCE'   , ''    , isbc = true },
 	['B.C.E.']     = { 'B.C.E.', ''    , isbc = true },
 	['AD']         = { 'BC'    , 'AD'   },
 	['A.D.']       = { 'B.C.'  , 'A.D.' },
 	['CE']         = { 'BCE'   , 'CE'   },
 	['C.E.']       = { 'B.C.E.', 'C.E.' },
 }
 
 local function get_era_for_year(era, year)
 	return (era_text[era] or era_text['BC'])[year &gt; 0 and 2 or 1] or ''
 end
 
 local function strftime(date, format, options)
 	-- Return date formatted as a string using codes similar to those
 	-- in the C strftime library function.
 	local sformat = string.format
 	local shortcuts = {
 		['%c'] = '%-I:%M %p %-d %B %-Y %{era}',  -- date and time: 2:30 pm 1 April 2016
 		['%x'] = '%-d %B %-Y %{era}',            -- date:          1 April 2016
 		['%X'] = '%-I:%M %p',                    -- time:          2:30 pm
 	}
 	if shortcuts[format] then
 		format = shortcuts[format]
 	end
 	local codes = {
 		a = { field = 'dayabbr' },
 		A = { field = 'dayname' },
 		b = { field = 'monthabbr' },
 		B = { field = 'monthname' },
 		u = { fmt = '%d'  , field = 'dowiso' },
 		w = { fmt = '%d'  , field = 'dow' },
 		d = { fmt = '%02d', fmt2 = '%d', field = 'day' },
 		m = { fmt = '%02d', fmt2 = '%d', field = 'month' },
 		Y = { fmt = '%04d', fmt2 = '%d', field = 'year' },
 		H = { fmt = '%02d', fmt2 = '%d', field = 'hour' },
 		M = { fmt = '%02d', fmt2 = '%d', field = 'minute' },
 		S = { fmt = '%02d', fmt2 = '%d', field = 'second' },
 		j = { fmt = '%03d', fmt2 = '%d', field = 'dayofyear' },
 		I = { fmt = '%02d', fmt2 = '%d', field = 'hour', special = 'hour12' },
 		p = { field = 'hour', special = 'am' },
 	}
 	options = make_option_table(options, date.options)
 	local amopt = options.am
 	local eraopt = options.era
 	local function replace_code(spaces, modifier, id)
 		local code = codes[id]
 		if code then
 			local fmt = code.fmt
 			if modifier == '-' and code.fmt2 then
 				fmt = code.fmt2
 			end
 			local value = date[code.field]
 			if not value then
 				return nil  -- an undefined field in a partial date
 			end
 			local special = code.special
 			if special then
 				if special == 'hour12' then
 					value = value % 12
 					value = value == 0 and 12 or value
 				elseif special == 'am' then
 					local ap = ({
 						['a.m.'] = { 'a.m.', 'p.m.' },
 						['AM'] = { 'AM', 'PM' },
 						['A.M.'] = { 'A.M.', 'P.M.' },
 					})[ampm_options[amopt]] or { 'am', 'pm' }
 					return (spaces == '' and '' or '&amp;nbsp;') .. (value &lt; 12 and ap[1] or ap[2])
 				end
 			end
 			if code.field == 'year' then
 				local sign = (era_text[eraopt] or {}).sign
 				if not sign or format:find('%{era}', 1, true) then
 					sign = ''
 					if value &lt;= 0 then
 						value = 1 - value
 					end
 				else
 					if value &gt;= 0 then
 						sign = ''
 					else
 						value = -value
 					end
 				end
 				return spaces .. sign .. sformat(fmt, value)
 			end
 			return spaces .. (fmt and sformat(fmt, value) or value)
 		end
 	end
 	local function replace_property(spaces, id)
 		if id == 'era' then
 			-- Special case so can use local era option.
 			local result = get_era_for_year(eraopt, date.year)
 			if result == '' then
 				return ''
 			end
 			return (spaces == '' and '' or '&amp;nbsp;') .. result
 		end
 		local result = date[id]
 		if type(result) == 'string' then
 			return spaces .. result
 		end
 		if type(result) == 'number' then
 			return  spaces .. tostring(result)
 		end
 		if type(result) == 'boolean' then
 			return  spaces .. (result and '1' or '0')
 		end
 		-- This occurs if id is an undefined field in a partial date, or is the name of a function.
 		return nil
 	end
 	local PERCENT = '\127PERCENT\127'
 	return (format
 		:gsub('%%%%', PERCENT)
 		:gsub('(%s*)%%{(%w+)}', replace_property)
 		:gsub('(%s*)%%(%-?)(%a)', replace_code)
 		:gsub(PERCENT, '%%')
 	)
 end
 
 local function _date_text(date, fmt, options)
 	-- Return a formatted string representing the given date.
 	if not is_date(date) then
 		error('date:text: need a date (use &quot;date:text()&quot; with a colon)', 2)
 	end
 	if type(fmt) == 'string' and fmt:match('%S') then
 		if fmt:find('%', 1, true) then
 			return strftime(date, fmt, options)
 		end
 	elseif date.partial then
 		fmt = date.month and 'my' or 'y'
 	else
 		fmt = 'dmy'
 		if date.hastime then
 			fmt = (date.second &gt; 0 and 'hms ' or 'hm ') .. fmt
 		end
 	end
 	local function bad_format()
 		-- For consistency with other format processing, return given format
 		-- (or cleaned format if original was not a string) if invalid.
 		return mw.text.nowiki(fmt)
 	end
 	if date.partial then
 		-- Ignore days in standard formats like 'ymd'.
 		if fmt == 'ym' or fmt == 'ymd' then
 			fmt = date.month and '%Y-%m %{era}' or '%Y %{era}'
 		elseif fmt == 'my' or fmt == 'dmy' or fmt == 'mdy' then
 			fmt = date.month and '%B %-Y %{era}' or '%-Y %{era}'
 		elseif fmt == 'y' then
 			fmt = date.month and '%-Y %{era}' or '%-Y %{era}'
 		else
 			return bad_format()
 		end
 		return strftime(date, fmt, options)
 	end
 	local function hm_fmt()
 		local plain = make_option_table(options, date.options).bydefault.am
 		return plain and '%H:%M' or '%-I:%M %p'
 	end
 	local need_time = date.hastime
 	local t = collection()
 	for item in fmt:gmatch('%S+') do
 		local f
 		if item == 'hm' then
 			f = hm_fmt()
 			need_time = false
 		elseif item == 'hms' then
 			f = '%H:%M:%S'
 			need_time = false
 		elseif item == 'ymd' then
 			f = '%Y-%m-%d %{era}'
 		elseif item == 'mdy' then
 			f = '%B %-d, %-Y %{era}'
 		elseif item == 'dmy' then
 			f = '%-d %B %-Y %{era}'
 		else
 			return bad_format()
 		end
 		t:add(f)
 	end
 	fmt = t:join(' ')
 	if need_time then
 		fmt = hm_fmt() .. ' ' .. fmt
 	end
 	return strftime(date, fmt, options)
 end
 
 local day_info = {
 	-- 0=Sun to 6=Sat
 	[0] = { 'Sun', 'Sunday' },
 	{ 'Mon', 'Monday' },
 	{ 'Tue', 'Tuesday' },
 	{ 'Wed', 'Wednesday' },
 	{ 'Thu', 'Thursday' },
 	{ 'Fri', 'Friday' },
 	{ 'Sat', 'Saturday' },
 }
 
 local month_info = {
 	-- 1=Jan to 12=Dec
 	{ 'Jan', 'January' },
 	{ 'Feb', 'February' },
 	{ 'Mar', 'March' },
 	{ 'Apr', 'April' },
 	{ 'May', 'May' },
 	{ 'Jun', 'June' },
 	{ 'Jul', 'July' },
 	{ 'Aug', 'August' },
 	{ 'Sep', 'September' },
 	{ 'Oct', 'October' },
 	{ 'Nov', 'November' },
 	{ 'Dec', 'December' },
 }
 
 local function name_to_number(text, translate)
 	if type(text) == 'string' then
 		return translate[text:lower()]
 	end
 end
 
 local function day_number(text)
 	return name_to_number(text, {
 		sun = 0, sunday = 0,
 		mon = 1, monday = 1,
 		tue = 2, tuesday = 2,
 		wed = 3, wednesday = 3,
 		thu = 4, thursday = 4,
 		fri = 5, friday = 5,
 		sat = 6, saturday = 6,
 	})
 end
 
 local function month_number(text)
 	return name_to_number(text, {
 		jan = 1, january = 1,
 		feb = 2, february = 2,
 		mar = 3, march = 3,
 		apr = 4, april = 4,
 		may = 5,
 		jun = 6, june = 6,
 		jul = 7, july = 7,
 		aug = 8, august = 8,
 		sep = 9, september = 9, sept = 9,
 		oct = 10, october = 10,
 		nov = 11, november = 11,
 		dec = 12, december = 12,
 	})
 end
 
 local function _list_text(list, fmt)
 	-- Return a list of formatted strings from a list of dates.
 	if not type(list) == 'table' then
 		error('date:list:text: need &quot;list:text()&quot; with a colon', 2)
 	end
 	local result = { join = _list_join }
 	for i, date in ipairs(list) do
 		result[i] = date:text(fmt)
 	end
 	return result
 end
 
 local function _date_list(date, spec)
 	-- Return a possibly empty numbered table of dates meeting the specification.
 	-- Dates in the list are in ascending order (oldest date first).
 	-- The spec should be a string of form &quot;&lt;count&gt; &lt;day&gt; &lt;op&gt;&quot;
 	-- where each item is optional and
 	--   count = number of items wanted in list
 	--   day = abbreviation or name such as Mon or Monday
 	--   op = &gt;, &gt;=, &lt;, &lt;= (default is &gt; meaning after date)
 	-- If no count is given, the list is for the specified days in date's month.
 	-- The default day is date's day.
 	-- The spec can also be a positive or negative number:
 	--   -5 is equivalent to '5 &lt;'
 	--   5  is equivalent to '5' which is '5 &gt;'
 	if not is_date(date) then
 		error('date:list: need a date (use &quot;date:list()&quot; with a colon)', 2)
 	end
 	local list = { text = _list_text }
 	if date.partial then
 		return list
 	end
 	local count, offset, operation
 	local ops = {
 		['&gt;='] = { before = false, include = true  },
 		['&gt;']  = { before = false, include = false },
 		['&lt;='] = { before = true , include = true  },
 		['&lt;']  = { before = true , include = false },
 	}
 	if spec then
 		if type(spec) == 'number' then
 			count = floor(spec + 0.5)
 			if count &lt; 0 then
 				count = -count
 				operation = ops['&lt;']
 			end
 		elseif type(spec) == 'string' then
 			local num, day, op = spec:match('^%s*(%d*)%s*(%a*)%s*([&lt;&gt;=]*)%s*$')
 			if not num then
 				return list
 			end
 			if num ~= '' then
 				count = tonumber(num)
 			end
 			if day ~= '' then
 				local dow = day_number(day:gsub('[sS]$', ''))  -- accept plural days
 				if not dow then
 					return list
 				end
 				offset = dow - date.dow
 			end
 			operation = ops[op]
 		else
 			return list
 		end
 	end
 	offset = offset or 0
 	operation = operation or ops['&gt;']
 	local datefrom, dayfirst, daylast
 	if operation.before then
 		if offset &gt; 0 or (offset == 0 and not operation.include) then
 			offset = offset - 7
 		end
 		if count then
 			if count &gt; 1 then
 				offset = offset - 7*(count - 1)
 			end
 			datefrom = date + offset
 		else
 			daylast = date.day + offset
 			dayfirst = daylast % 7
 			if dayfirst == 0 then
 				dayfirst = 7
 			end
 		end
 	else
 		if offset &lt; 0 or (offset == 0 and not operation.include) then
 			offset = offset + 7
 		end
 		if count then
 			datefrom = date + offset
 		else
 			dayfirst = date.day + offset
 			daylast = date.monthdays
 		end
 	end
 	if not count then
 		if daylast &lt; dayfirst then
 			return list
 		end
 		count = floor((daylast - dayfirst)/7) + 1
 		datefrom = Date(date, {day = dayfirst})
 	end
 	for i = 1, count do
 		if not datefrom then break end  -- exceeds date limits
 		list[i] = datefrom
 		datefrom = datefrom + 7
 	end
 	return list
 end
 
 -- A table to get the current date/time (UTC), but only if needed.
 local current = setmetatable({}, {
 	__index = function (self, key)
 		local d = os.date('!*t')
 		self.year = d.year
 		self.month = d.month
 		self.day = d.day
 		self.hour = d.hour
 		self.minute = d.min
 		self.second = d.sec
 		return rawget(self, key)
 	end })
 
 local function extract_date(newdate, text)
 	-- Parse the date/time in text and return n, o where
 	--   n = table of numbers with date/time fields
 	--   o = table of options for AM/PM or AD/BC or format, if any
 	-- or return nothing if date is known to be invalid.
 	-- Caller determines if the values in n are valid.
 	-- A year must be positive ('1' to '9999'); use 'BC' for BC.
 	-- In a y-m-d string, the year must be four digits to avoid ambiguity
 	-- ('0001' to '9999'). The only way to enter year &lt;= 0 is by specifying
 	-- the date as three numeric parameters like ymd Date(-1, 1, 1).
 	-- Dates of form d/m/y, m/d/y, y/m/d are rejected as potentially ambiguous.
 	local date, options = {}, {}
 	if text:sub(-1) == 'Z' then
 		-- Extract date/time from a Wikidata timestamp.
 		-- The year can be 1 to 16 digits but this module handles 1 to 4 digits only.
 		-- Examples: '+2016-06-21T14:30:00Z', '-0000000180-00-00T00:00:00Z'.
 		local sign, y, m, d, H, M, S = text:match('^([+%-])(%d+)%-(%d%d)%-(%d%d)T(%d%d):(%d%d):(%d%d)Z$')
 		if sign then
 			y = tonumber(y)
 			if sign == '-' and y &gt; 0 then
 				y = -y
 			end
 			if y &lt;= 0 then
 				options.era = 'BCE'
 			end
 			date.year = y
 			m = tonumber(m)
 			d = tonumber(d)
 			H = tonumber(H)
 			M = tonumber(M)
 			S = tonumber(S)
 			if m == 0 then
 				newdate.partial = true
 				return date, options
 			end
 			date.month = m
 			if d == 0 then
 				newdate.partial = true
 				return date, options
 			end
 			date.day = d
 			if H &gt; 0 or M &gt; 0 or S &gt; 0 then
 				date.hour = H
 				date.minute = M
 				date.second = S
 			end
 			return date, options
 		end
 		return
 	end
 	local function extract_ymd(item)
 		-- Called when no day or month has been set.
 		local y, m, d = item:match('^(%d%d%d%d)%-(%w+)%-(%d%d?)$')
 		if y then
 			if date.year then
 				return
 			end
 			if m:match('^%d%d?$') then
 				m = tonumber(m)
 			else
 				m = month_number(m)
 			end
 			if m then
 				date.year = tonumber(y)
 				date.month = m
 				date.day = tonumber(d)
 				return true
 			end
 		end
 	end
 	local function extract_day_or_year(item)
 		-- Called when a day would be valid, or
 		-- when a year would be valid if no year has been set and partial is set.
 		local number, suffix = item:match('^(%d%d?%d?%d?)(.*)$')
 		if number then
 			local n = tonumber(number)
 			if #number &lt;= 2 and n &lt;= 31 then
 				suffix = suffix:lower()
 				if suffix == '' or suffix == 'st' or suffix == 'nd' or suffix == 'rd' or suffix == 'th' then
 					date.day = n
 					return true
 				end
 			elseif suffix == '' and newdate.partial and not date.year then
 				date.year = n
 				return true
 			end
 		end
 	end
 	local function extract_month(item)
 		-- A month must be given as a name or abbreviation; a number could be ambiguous.
 		local m = month_number(item)
 		if m then
 			date.month = m
 			return true
 		end
 	end
 	local function extract_time(item)
 		local h, m, s = item:match('^(%d%d?):(%d%d)(:?%d*)$')
 		if date.hour or not h then
 			return
 		end
 		if s ~= '' then
 			s = s:match('^:(%d%d)$')
 			if not s then
 				return
 			end
 		end
 		date.hour = tonumber(h)
 		date.minute = tonumber(m)
 		date.second = tonumber(s)  -- nil if empty string
 		return true
 	end
 	local item_count = 0
 	local index_time
 	local function set_ampm(item)
 		local H = date.hour
 		if H and not options.am and index_time + 1 == item_count then
 			options.am = ampm_options[item]  -- caller checked this is not nil
 			if item:match('^[Aa]') then
 				if not (1 &lt;= H and H &lt;= 12) then
 					return
 				end
 				if H == 12 then
 					date.hour = 0
 				end
 			else
 				if not (1 &lt;= H and H &lt;= 23) then
 					return
 				end
 				if H &lt;= 11 then
 					date.hour = H + 12
 				end
 			end
 			return true
 		end
 	end
 	for item in text:gsub(',', ' '):gsub('&amp;nbsp;', ' '):gmatch('%S+') do
 		item_count = item_count + 1
 		if era_text[item] then
 			-- Era is accepted in peculiar places.
 			if options.era then
 				return
 			end
 			options.era = item
 		elseif ampm_options[item] then
 			if not set_ampm(item) then
 				return
 			end
 		elseif item:find(':', 1, true) then
 			if not extract_time(item) then
 				return
 			end
 			index_time = item_count
 		elseif date.day and date.month then
 			if date.year then
 				return  -- should be nothing more so item is invalid
 			end
 			if not item:match('^(%d%d?%d?%d?)$') then
 				return
 			end
 			date.year = tonumber(item)
 		elseif date.day then
 			if not extract_month(item) then
 				return
 			end
 		elseif date.month then
 			if not extract_day_or_year(item) then
 				return
 			end
 		elseif extract_month(item) then
 			options.format = 'mdy'
 		elseif extract_ymd(item) then
 			options.format = 'ymd'
 		elseif extract_day_or_year(item) then
 			if date.day then
 				options.format = 'dmy'
 			end
 		else
 			return
 		end
 	end
 	if not date.year or date.year == 0 then
 		return
 	end
 	local era = era_text[options.era]
 	if era and era.isbc then
 		date.year = 1 - date.year
 	end
 	return date, options
 end
 
 local function autofill(date1, date2)
 	-- Fill any missing month or day in each date using the
 	-- corresponding component from the other date, if present,
 	-- or with 1 if both dates are missing the month or day.
 	-- This gives a good result for calculating the difference
 	-- between two partial dates when no range is wanted.
 	-- Return filled date1, date2 (two full dates).
 	local function filled(a, b)
 		local fillmonth, fillday
 		if not a.month then
 			fillmonth = b.month or 1
 		end
 		if not a.day then
 			fillday = b.day or 1
 		end
 		if fillmonth or fillday then  -- need to create a new date
 			if (fillmonth or a.month) == 2 and (fillday or a.day) == 29 then
 				-- Avoid invalid date, for example with {{age|2013|29 Feb 2016}} or {{age|Feb 2013|29 Jan 2015}}.
 				if not is_leap_year(a.year, a.calendar) then
 					fillday = 28
 				end
 			end
 			a = Date(a, { month = fillmonth, day = fillday })
 		end
 		return a
 	end
 	return filled(date1, date2), filled(date2, date1)
 end
 
 local function date_add_sub(lhs, rhs, is_sub)
 	-- Return a new date from calculating (lhs + rhs) or (lhs - rhs),
 	-- or return nothing if invalid.
 	-- The result is nil if the calculated date exceeds allowable limits.
 	-- Caller ensures that lhs is a date; its properties are copied for the new date.
 	if lhs.partial then
 		-- Adding to a partial is not supported.
 		-- Can subtract a date or partial from a partial, but this is not called for that.
 		return
 	end
 	local function is_prefix(text, word, minlen)
 		local n = #text
 		return (minlen or 1) &lt;= n and n &lt;= #word and text == word:sub(1, n)
 	end
 	local function do_days(n)
 		local forcetime, jd
 		if floor(n) == n then
 			jd = lhs.jd
 		else
 			forcetime = not lhs.hastime
 			jd = lhs.jdz
 		end
 		jd = jd + (is_sub and -n or n)
 		if forcetime then
 			jd = tostring(jd)
 			if not jd:find('.', 1, true) then
 				jd = jd .. '.0'
 			end
 		end
 		return Date(lhs, 'juliandate', jd)
 	end
 	if type(rhs) == 'number' then
 		-- Add/subtract days, including fractional days.
 		return do_days(rhs)
 	end
 	if type(rhs) == 'string' then
 		-- rhs is a single component like '26m' or '26 months' (with optional sign).
 		-- Fractions like '3.25d' are accepted for the units which are handled as days.
 		local sign, numstr, id = rhs:match('^%s*([+-]?)([%d%.]+)%s*(%a+)$')
 		if sign then
 			if sign == '-' then
 				is_sub = not (is_sub and true or false)
 			end
 			local y, m, days
 			local num = tonumber(numstr)
 			if not num then
 				return
 			end
 			id = id:lower()
 			if is_prefix(id, 'years') then
 				y = num
 				m = 0
 			elseif is_prefix(id, 'months') then
 				y = floor(num / 12)
 				m = num % 12
 			elseif is_prefix(id, 'weeks') then
 				days = num * 7
 			elseif is_prefix(id, 'days') then
 				days = num
 			elseif is_prefix(id, 'hours') then
 				days = num / 24
 			elseif is_prefix(id, 'minutes', 3) then
 				days = num / (24 * 60)
 			elseif is_prefix(id, 'seconds') then
 				days = num / (24 * 3600)
 			else
 				return
 			end
 			if days then
 				return do_days(days)
 			end
 			if numstr:find('.', 1, true) then
 				return
 			end
 			if is_sub then
 				y = -y
 				m = -m
 			end
 			assert(-11 &lt;= m and m &lt;= 11)
 			y = lhs.year + y
 			m = lhs.month + m
 			if m &gt; 12 then
 				y = y + 1
 				m = m - 12
 			elseif m &lt; 1 then
 				y = y - 1
 				m = m + 12
 			end
 			local d = math.min(lhs.day, days_in_month(y, m, lhs.calendar))
 			return Date(lhs, y, m, d)
 		end
 	end
 	if is_diff(rhs) then
 		local days = rhs.age_days
 		if (is_sub or false) ~= (rhs.isnegative or false) then
 			days = -days
 		end
 		return lhs + days
 	end
 end
 
 local full_date_only = {
 	dayabbr = true,
 	dayname = true,
 	dow = true,
 	dayofweek = true,
 	dowiso = true,
 	dayofweekiso = true,
 	dayofyear = true,
 	gsd = true,
 	juliandate = true,
 	jd = true,
 	jdz = true,
 	jdnoon = true,
 }
 
 -- Metatable for a date's calculated fields.
 local datemt = {
 	__index = function (self, key)
 		if rawget(self, 'partial') then
 			if full_date_only[key] then return end
 			if key == 'monthabbr' or key == 'monthdays' or key == 'monthname' then
 				if not self.month then return end
 			end
 		end
 		local value
 		if key == 'dayabbr' then
 			value = day_info[self.dow][1]
 		elseif key == 'dayname' then
 			value = day_info[self.dow][2]
 		elseif key == 'dow' then
 			value = (self.jdnoon + 1) % 7  -- day-of-week 0=Sun to 6=Sat
 		elseif key == 'dayofweek' then
 			value = self.dow
 		elseif key == 'dowiso' then
 			value = (self.jdnoon % 7) + 1  -- ISO day-of-week 1=Mon to 7=Sun
 		elseif key == 'dayofweekiso' then
 			value = self.dowiso
 		elseif key == 'dayofyear' then
 			local first = Date(self.year, 1, 1, self.calendar).jdnoon
 			value = self.jdnoon - first + 1  -- day-of-year 1 to 366
 		elseif key == 'era' then
 			-- Era text (never a negative sign) from year and options.
 			value = get_era_for_year(self.options.era, self.year)
 		elseif key == 'format' then
 			value = self.options.format or 'dmy'
 		elseif key == 'gsd' then
 			-- GSD = 1 from 00:00:00 to 23:59:59 on 1 January 1 AD Gregorian calendar,
 			-- which is from jd 1721425.5 to 1721426.49999.
 			value = floor(self.jd - 1721424.5)
 		elseif key == 'juliandate' or key == 'jd' or key == 'jdz' then
 			local jd, jdz = julian_date(self)
 			rawset(self, 'juliandate', jd)
 			rawset(self, 'jd', jd)
 			rawset(self, 'jdz', jdz)
 			return key == 'jdz' and jdz or jd
 		elseif key == 'jdnoon' then
 			-- Julian date at noon (an integer) on the calendar day when jd occurs.
 			value = floor(self.jd + 0.5)
 		elseif key == 'isleapyear' then
 			value = is_leap_year(self.year, self.calendar)
 		elseif key == 'monthabbr' then
 			value = month_info[self.month][1]
 		elseif key == 'monthdays' then
 			value = days_in_month(self.year, self.month, self.calendar)
 		elseif key == 'monthname' then
 			value = month_info[self.month][2]
 		end
 		if value ~= nil then
 			rawset(self, key, value)
 			return value
 		end
 	end,
 }
 
 -- Date operators.
 local function mt_date_add(lhs, rhs)
 	if not is_date(lhs) then
 		lhs, rhs = rhs, lhs  -- put date on left (it must be a date for this to have been called)
 	end
 	return date_add_sub(lhs, rhs)
 end
 
 local function mt_date_sub(lhs, rhs)
 	if is_date(lhs) then
 		if is_date(rhs) then
 			return DateDiff(lhs, rhs)
 		end
 		return date_add_sub(lhs, rhs, true)
 	end
 end
 
 local function mt_date_concat(lhs, rhs)
 	return tostring(lhs) .. tostring(rhs)
 end
 
 local function mt_date_tostring(self)
 	return self:text()
 end
 
 local function mt_date_eq(lhs, rhs)
 	-- Return true if dates identify same date/time where, for example,
 	-- Date(-4712, 1, 1, 'Julian') == Date(-4713, 11, 24, 'Gregorian') is true.
 	-- This is called only if lhs and rhs have the same type and the same metamethod.
 	if lhs.partial or rhs.partial then
 		-- One date is partial; the other is a partial or a full date.
 		-- The months may both be nil, but must be the same.
 		return lhs.year == rhs.year and lhs.month == rhs.month and lhs.calendar == rhs.calendar
 	end
 	return lhs.jdz == rhs.jdz
 end
 
 local function mt_date_lt(lhs, rhs)
 	-- Return true if lhs &lt; rhs, for example,
 	-- Date('1 Jan 2016') &lt; Date('06:00 1 Jan 2016') is true.
 	-- This is called only if lhs and rhs have the same type and the same metamethod.
 	if lhs.partial or rhs.partial then
 		-- One date is partial; the other is a partial or a full date.
 		if lhs.calendar ~= rhs.calendar then
 			return lhs.calendar == 'Julian'
 		end
 		if lhs.partial then
 			lhs = lhs.partial.first
 		end
 		if rhs.partial then
 			rhs = rhs.partial.first
 		end
 	end
 	return lhs.jdz &lt; rhs.jdz
 end
 
 --[[ Examples of syntax to construct a date:
 Date(y, m, d, 'julian')             default calendar is 'gregorian'
 Date(y, m, d, H, M, S, 'julian')
 Date('juliandate', jd, 'julian')    if jd contains &quot;.&quot; text output includes H:M:S
 Date('currentdate')
 Date('currentdatetime')
 Date('1 April 1995', 'julian')      parse date from text
 Date('1 April 1995 AD', 'julian')   using an era sets a flag to do the same for output
 Date('04:30:59 1 April 1995', 'julian')
 Date(date)                          copy of an existing date
 Date(date, t)                       same, updated with y,m,d,H,M,S fields from table t
 Date(t)                       		date with y,m,d,H,M,S fields from table t
 ]]
 function Date(...)  -- for forward declaration above
 	-- Return a table holding a date assuming a uniform calendar always applies
 	-- (proleptic Gregorian calendar or proleptic Julian calendar), or
 	-- return nothing if date is invalid.
 	-- A partial date has a valid year, however its month may be nil, and
 	-- its day and time fields are nil.
 	-- Field partial is set to false (if a full date) or a table (if a partial date).
 	local calendars = { julian = 'Julian', gregorian = 'Gregorian' }
 	local newdate = {
 		_id = uniq,
 		calendar = 'Gregorian',  -- default is Gregorian calendar
 		hastime = false,  -- true if input sets a time
 		hour = 0,  -- always set hour/minute/second so don't have to handle nil
 		minute = 0,
 		second = 0,
 		options = {},
 		list = _date_list,
 		subtract = function (self, rhs, options)
 			return DateDiff(self, rhs, options)
 		end,
 		text = _date_text,
 	}
 	local argtype, datetext, is_copy, jd_number, tnums
 	local numindex = 0
 	local numfields = { 'year', 'month', 'day', 'hour', 'minute', 'second' }
 	local numbers = {}
 	for _, v in ipairs({...}) do
 		v = strip_to_nil(v)
 		local vlower = type(v) == 'string' and v:lower() or nil
 		if v == nil then
 			-- Ignore empty arguments after stripping so modules can directly pass template parameters.
 		elseif calendars[vlower] then
 			newdate.calendar = calendars[vlower]
 		elseif vlower == 'partial' then
 			newdate.partial = true
 		elseif vlower == 'fix' then
 			newdate.want_fix = true
 		elseif is_date(v) then
 			-- Copy existing date (items can be overridden by other arguments).
 			if is_copy or tnums then
 				return
 			end
 			is_copy = true
 			newdate.calendar = v.calendar
 			newdate.partial = v.partial
 			newdate.hastime = v.hastime
 			newdate.options = v.options
 			newdate.year = v.year
 			newdate.month = v.month
 			newdate.day = v.day
 			newdate.hour = v.hour
 			newdate.minute = v.minute
 			newdate.second = v.second
 		elseif type(v) == 'table' then
 			if tnums then
 				return
 			end
 			tnums = {}
 			local tfields = { year=1, month=1, day=1, hour=2, minute=2, second=2 }
 			for tk, tv in pairs(v) do
 				if tfields[tk] then
 					tnums[tk] = tonumber(tv)
 				end
 				if tfields[tk] == 2 then
 					newdate.hastime = true
 				end
 			end
 		else
 			local num = tonumber(v)
 			if not num and argtype == 'setdate' and numindex == 1 then
 				num = month_number(v)
 			end
 			if num then
 				if not argtype then
 					argtype = 'setdate'
 				end
 				if argtype == 'setdate' and numindex &lt; 6 then
 					numindex = numindex + 1
 					numbers[numfields[numindex]] = num
 				elseif argtype == 'juliandate' and not jd_number then
 					jd_number = num
 					if type(v) == 'string' then
 						if v:find('.', 1, true) then
 							newdate.hastime = true
 						end
 					elseif num ~= floor(num) then
 						-- The given value was a number. The time will be used
 						-- if the fractional part is nonzero.
 						newdate.hastime = true
 					end
 				else
 					return
 				end
 			elseif argtype then
 				return
 			elseif type(v) == 'string' then
 				if v == 'currentdate' or v == 'currentdatetime' or v == 'juliandate' then
 					argtype = v
 				else
 					argtype = 'datetext'
 					datetext = v
 				end
 			else
 				return
 			end
 		end
 	end
 	if argtype == 'datetext' then
 		if tnums or not set_date_from_numbers(newdate, extract_date(newdate, datetext)) then
 			return
 		end
 	elseif argtype == 'juliandate' then
 		newdate.partial = nil
 		newdate.jd = jd_number
 		if not set_date_from_jd(newdate) then
 			return
 		end
 	elseif argtype == 'currentdate' or argtype == 'currentdatetime' then
 		newdate.partial = nil
 		newdate.year = current.year
 		newdate.month = current.month
 		newdate.day = current.day
 		if argtype == 'currentdatetime' then
 			newdate.hour = current.hour
 			newdate.minute = current.minute
 			newdate.second = current.second
 			newdate.hastime = true
 		end
 		newdate.calendar = 'Gregorian'  -- ignore any given calendar name
 	elseif argtype == 'setdate' then
 		if tnums or not set_date_from_numbers(newdate, numbers) then
 			return
 		end
 	elseif not (is_copy or tnums) then
 		return
 	end
 	if tnums then
 		newdate.jd = nil  -- force recalculation in case jd was set before changes from tnums
 		if not set_date_from_numbers(newdate, tnums) then
 			return
 		end
 	end
 	if newdate.partial then
 		local year = newdate.year
 		local month = newdate.month
 		local first = Date(year, month or 1, 1, newdate.calendar)
 		month = month or 12
 		local last = Date(year, month, days_in_month(year, month), newdate.calendar)
 		newdate.partial = { first = first, last = last }
 	else
 		newdate.partial = false  -- avoid index lookup
 	end
 	setmetatable(newdate, datemt)
 	local readonly = {}
 	local mt = {
 		__index = newdate,
 		__newindex = function(t, k, v) error('date.' .. tostring(k) .. ' is read-only', 2) end,
 		__add = mt_date_add,
 		__sub = mt_date_sub,
 		__concat = mt_date_concat,
 		__tostring = mt_date_tostring,
 		__eq = mt_date_eq,
 		__lt = mt_date_lt,
 	}
 	return setmetatable(readonly, mt)
 end
 
 local function _diff_age(diff, code, options)
 	-- Return a tuple of integer values from diff as specified by code, except that
 	-- each integer may be a list of two integers for a diff with a partial date, or
 	-- return nil if the code is not supported.
 	-- If want round, the least significant unit is rounded to nearest whole unit.
 	-- For a duration, an extra day is added.
 	local wantround, wantduration, wantrange
 	if type(options) == 'table' then
 		wantround = options.round
 		wantduration = options.duration
 		wantrange = options.range
 	else
 		wantround = options
 	end
 	if not is_diff(diff) then
 		local f = wantduration and 'duration' or 'age'
 		error(f .. ': need a date difference (use &quot;diff:' .. f .. '()&quot; with a colon)', 2)
 	end
 	if diff.partial then
 		-- Ignore wantround, wantduration.
 		local function choose(v)
 			if type(v) == 'table' then
 				if not wantrange or v[1] == v[2] then
 					-- Example: Date('partial', 2005) - Date('partial', 2001) gives
 					-- diff.years = { 3, 4 } to show the range of possible results.
 					-- If do not want a range, choose the second value as more expected.
 					return v[2]
 				end
 			end
 			return v
 		end
 		if code == 'ym' or code == 'ymd' then
 			if not wantrange and diff.iszero then
 				-- This avoids an unexpected result such as
 				-- Date('partial', 2001) - Date('partial', 2001)
 				-- giving diff = { years = 0, months = { 0, 11 } }
 				-- which would be reported as 0 years and 11 months.
 				return 0, 0
 			end
 			return choose(diff.partial.years), choose(diff.partial.months)
 		end
 		if code == 'y' then
 			return choose(diff.partial.years)
 		end
 		if code == 'm' or code == 'w' or code == 'd' then
 			return choose({ diff.partial.mindiff:age(code), diff.partial.maxdiff:age(code) })
 		end
 		return nil
 	end
 	local extra_days = wantduration and 1 or 0
 	if code == 'wd' or code == 'w' or code == 'd' then
 		local offset = wantround and 0.5 or 0
 		local days = diff.age_days + extra_days
 		if code == 'wd' or code == 'd' then
 			days = floor(days + offset)
 			if code == 'd' then
 				return days
 			end
 			return floor(days/7), days % 7
 		end
 		return floor(days/7 + offset)
 	end
 	local H, M, S = diff.hours, diff.minutes, diff.seconds
 	if code == 'dh' or code == 'dhm' or code == 'dhms' or code == 'h' or code == 'hm' or code == 'hms' then
 		local days = floor(diff.age_days + extra_days)
 		local inc_hour
 		if wantround then
 			if code == 'dh' or code == 'h' then
 				if M &gt;= 30 then
 					inc_hour = true
 				end
 			elseif code == 'dhm' or code == 'hm' then
 				if S &gt;= 30 then
 					M = M + 1
 					if M &gt;= 60 then
 						M = 0
 						inc_hour = true
 					end
 				end
 			else
 				-- Nothing needed because S is an integer.
 			end
 			if inc_hour then
 				H = H + 1
 				if H &gt;= 24 then
 					H = 0
 					days = days + 1
 				end
 			end
 		end
 		if code == 'dh' or code == 'dhm' or code == 'dhms' then
 			if code == 'dh' then
 				return days, H
 			elseif code == 'dhm' then
 				return days, H, M
 			else
 				return days, H, M, S
 			end
 		end
 		local hours = days * 24 + H
 		if code == 'h' then
 			return hours
 		elseif code == 'hm' then
 			return hours, M
 		end
 		return hours, M, S
 	end
 	if wantround then
 		local inc_hour
 		if code == 'ymdh' or code == 'ymwdh' then
 			if M &gt;= 30 then
 				inc_hour = true
 			end
 		elseif code == 'ymdhm' or code == 'ymwdhm' then
 			if S &gt;= 30 then
 				M = M + 1
 				if M &gt;= 60 then
 					M = 0
 					inc_hour = true
 				end
 			end
 		elseif code == 'ymd' or code == 'ymwd' or code == 'yd' or code == 'md' then
 			if H &gt;= 12 then
 				extra_days = extra_days + 1
 			end
 		end
 		if inc_hour then
 			H = H + 1
 			if H &gt;= 24 then
 				H = 0
 				extra_days = extra_days + 1
 			end
 		end
 	end
 	local y, m, d = diff.years, diff.months, diff.days
 	if extra_days &gt; 0 then
 		d = d + extra_days
 		if d &gt; 28 or code == 'yd' then
 			-- Recalculate in case have passed a month.
 			diff = diff.date1 + extra_days - diff.date2
 			y, m, d = diff.years, diff.months, diff.days
 		end
 	end
 	if code == 'ymd' then
 		return y, m, d
 	elseif code == 'yd' then
 		if y &gt; 0 then
 			-- It is known that diff.date1 &gt; diff.date2.
 			diff = diff.date1 - (diff.date2 + (y .. 'y'))
 		end
 		return y, floor(diff.age_days)
 	elseif code == 'md' then
 		return y * 12 + m, d
 	elseif code == 'ym' or code == 'm' then
 		if wantround then
 			if d &gt;= 16 then
 				m = m + 1
 				if m &gt;= 12 then
 					m = 0
 					y = y + 1
 				end
 			end
 		end
 		if code == 'ym' then
 			return y, m
 		end
 		return y * 12 + m
 	elseif code == 'ymw' then
 		local weeks = floor(d/7)
 		if wantround then
 			local days = d % 7
 			if days &gt; 3 or (days == 3 and H &gt;= 12) then
 				weeks = weeks + 1
 			end
 		end
 		return y, m, weeks
 	elseif code == 'ymwd' then
 		return y, m, floor(d/7), d % 7
 	elseif code == 'ymdh' then
 		return y, m, d, H
 	elseif code == 'ymwdh' then
 		return y, m, floor(d/7), d % 7, H
 	elseif code == 'ymdhm' then
 		return y, m, d, H, M
 	elseif code == 'ymwdhm' then
 		return y, m, floor(d/7), d % 7, H, M
 	end
 	if code == 'y' then
 		if wantround and m &gt;= 6 then
 			y = y + 1
 		end
 		return y
 	end
 	return nil
 end
 
 local function _diff_duration(diff, code, options)
 	if type(options) ~= 'table' then
 		options = { round = options }
 	end
 	options.duration = true
 	return _diff_age(diff, code, options)
 end
 
 -- Metatable for some operations on date differences.
 diffmt = {  -- for forward declaration above
 	__concat = function (lhs, rhs)
 		return tostring(lhs) .. tostring(rhs)
 	end,
 	__tostring = function (self)
 		return tostring(self.age_days)
 	end,
 	__index = function (self, key)
 		local value
 		if key == 'age_days' then
 			if rawget(self, 'partial') then
 				local function jdz(date)
 					return (date.partial and date.partial.first or date).jdz
 				end
 				value = jdz(self.date1) - jdz(self.date2)
 			else
 				value = self.date1.jdz - self.date2.jdz
 			end
 		end
 		if value ~= nil then
 			rawset(self, key, value)
 			return value
 		end
 	end,
 }
 
 function DateDiff(date1, date2, options)  -- for forward declaration above
 	-- Return a table with the difference between two dates (date1 - date2).
 	-- The difference is negative if date1 is older than date2.
 	-- Return nothing if invalid.
 	-- If d = date1 - date2 then
 	--     date1 = date2 + d
 	-- If date1 &gt;= date2 and the dates have no H:M:S time specified then
 	--     date1 = date2 + (d.years..'y') + (d.months..'m') + d.days
 	-- where the larger time units are added first.
 	-- The result of Date(2015,1,x) + '1m' is Date(2015,2,28) for
 	-- x = 28, 29, 30, 31. That means, for example,
 	--     d = Date(2015,3,3) - Date(2015,1,31)
 	-- gives d.years, d.months, d.days = 0, 1, 3 (excluding date1).
 	if not (is_date(date1) and is_date(date2) and date1.calendar == date2.calendar) then
 		return
 	end
 	local wantfill
 	if type(options) == 'table' then
 		wantfill = options.fill
 	end
 	local isnegative = false
 	local iszero = false
 	if date1 &lt; date2 then
 		isnegative = true
 		date1, date2 = date2, date1
 	elseif date1 == date2 then
 		iszero = true
 	end
 	-- It is known that date1 &gt;= date2 (period is from date2 to date1).
 	if date1.partial or date2.partial then
 		-- Two partial dates might have timelines:
 		---------------------A=================B--- date1 is from A to B inclusive
 		--------C=======D-------------------------- date2 is from C to D inclusive
 		-- date1 &gt; date2 iff A &gt; C (date1.partial.first &gt; date2.partial.first)
 		-- The periods can overlap ('April 2001' - '2001'):
 		-------------A===B------------------------- A=2001-04-01  B=2001-04-30
 		--------C=====================D------------ C=2001-01-01  D=2001-12-31
 		if wantfill then
 			date1, date2 = autofill(date1, date2)
 		else
 			local function zdiff(date1, date2)
 				local diff = date1 - date2
 				if diff.isnegative then
 					return date1 - date1  -- a valid diff in case we call its methods
 				end
 				return diff
 			end
 			local function getdate(date, which)
 				return date.partial and date.partial[which] or date
 			end
 			local maxdiff = zdiff(getdate(date1, 'last'), getdate(date2, 'first'))
 			local mindiff = zdiff(getdate(date1, 'first'), getdate(date2, 'last'))
 			local years, months
 			if maxdiff.years == mindiff.years then
 				years = maxdiff.years
 				if maxdiff.months == mindiff.months then
 					months = maxdiff.months
 				else
 					months = { mindiff.months, maxdiff.months }
 				end
 			else
 				years = { mindiff.years, maxdiff.years }
 			end
 			return setmetatable({
 				date1 = date1,
 				date2 = date2,
 				partial = {
 					years = years,
 					months = months,
 					maxdiff = maxdiff,
 					mindiff = mindiff,
 				},
 				isnegative = isnegative,
 				iszero = iszero,
 				age = _diff_age,
 				duration = _diff_duration,
 			}, diffmt)
 		end
 	end
 	local y1, m1 = date1.year, date1.month
 	local y2, m2 = date2.year, date2.month
 	local years = y1 - y2
 	local months = m1 - m2
 	local d1 = date1.day + hms(date1)
 	local d2 = date2.day + hms(date2)
 	local days, time
 	if d1 &gt;= d2 then
 		days = d1 - d2
 	else
 		months = months - 1
 		-- Get days in previous month (before the &quot;to&quot; date) given December has 31 days.
 		local dpm = m1 &gt; 1 and days_in_month(y1, m1 - 1, date1.calendar) or 31
 		if d2 &gt;= dpm then
 			days = d1 - hms(date2)
 		else
 			days = dpm - d2 + d1
 		end
 	end
 	if months &lt; 0 then
 		years = years - 1
 		months = months + 12
 	end
 	days, time = math.modf(days)
 	local H, M, S = h_m_s(time)
 	return setmetatable({
 		date1 = date1,
 		date2 = date2,
 		partial = false,  -- avoid index lookup
 		years = years,
 		months = months,
 		days = days,
 		hours = H,
 		minutes = M,
 		seconds = S,
 		isnegative = isnegative,
 		iszero = iszero,
 		age = _diff_age,
 		duration = _diff_duration,
 	}, diffmt)
 end
 
 return {
 	_current = current,
 	_Date = Date,
 	_days_in_month = days_in_month,