Module:Date: Difference between revisions

    From Nonbinary Wiki
    (enhanced version of Module:Age which will be replaced by this module as it provides generic date functions)
     
    (formatted output and strftime)
    Line 45: Line 45:
    local function is_leap_year(year, calname)
    local function is_leap_year(year, calname)
    -- Return true if year is a leap year.
    -- Return true if year is a leap year.
    if calname == 'JCAL' then
    if calname == 'Julian' then
    return year % 4 == 0
    return year % 4 == 0
    end
    end
    Line 66: Line 66:
    -- http://www.tondering.dk/claus/cal/julperiod.php#formula
    -- http://www.tondering.dk/claus/cal/julperiod.php#formula
    -- Testing shows this works for all dates from year -9999 to 9999!
    -- Testing shows this works for all dates from year -9999 to 9999!
    -- JDN 0 is the 24-hour period starting at noon UTC on
    -- JDN 0 is the 24-hour period starting at noon UTC on Monday
    --    1 January 4713 BC  = (-4712, 1, 1)  Julian calendar
    --    1 January 4713 BC  = (-4712, 1, 1)  Julian calendar
    --  24 November 4714 BC = (-4713, 11, 24) Gregorian calendar
    --  24 November 4714 BC = (-4713, 11, 24) Gregorian calendar
    Line 76: Line 76:
    local a = floor((14 - date.month)/12)
    local a = floor((14 - date.month)/12)
    local y = date.year + 4800 - a
    local y = date.year + 4800 - a
    if date.calname == 'JCAL' then
    if date.calname == 'Julian' then
    offset = floor(y/4) - 32083
    offset = floor(y/4) - 32083
    else
    else
    Line 104: Line 104:
    local jd = date.jd
    local jd = date.jd
    local limits  -- min/max limits for date ranges −9999-01-01 to 9999-12-31
    local limits  -- min/max limits for date ranges −9999-01-01 to 9999-12-31
    if calname == 'JCAL' then
    if calname == 'Julian' then
    limits = { -1931076.5, 5373557.5 }
    limits = { -1931076.5, 5373557.49999 }
    elseif calname == 'GCAL' then
    elseif calname == 'Gregorian' then
    limits = { -1930999.5, 5373484.5 }
    limits = { -1930999.5, 5373484.49999 }
    else
    else
    limits = { 1, 0 }  -- impossible
    limits = { 1, 0 }  -- impossible
    end
    end
    if not (limits[1] <= jd and jd < limits[2]) then
    if not (limits[1] <= jd and jd <= limits[2]) then
    date.isvalid = false
    date.isvalid = false
    return
    return
    Line 138: Line 138:
    end
    end
    local b, c
    local b, c
    if calname == 'JCAL' then
    if calname == 'Julian' then
    b = 0
    b = 0
    c = jdn + 32082
    c = jdn + 32082
    Line 154: Line 154:
    end
    end


    local function date_text(date)
    local function make_option_table(options)
    -- Return formatted string from given date.
    -- If options is a string, return a table with its settings.
    -- Otherwise return options (it should already be a table).
    if type(options) == 'string' then
    -- Example: 'am:AM era:BC'
    local result = {}
    for item in options:gmatch('%S+') do
    local lhs, rhs = item:match('^(%w+):(.*)$')
    if lhs then
    result[lhs] = rhs
    end
    end
    return result
    end
    return options
    end
     
    local function strftime(date, format, options)
    -- Return date formatted as a string using codes similar to those
    -- in the C strftime library function.
    if not date.isvalid then
    if not date.isvalid then
    return '(invalid)'
    return '(invalid)'
    end
    end
    local time = ''
    local codes = {
    if date.hastime then
    a = { field = 'dayabbr' },
    if date.second > 0 then
    A = { field = 'dayname' },
    time = string.format(' %02d:%02d:%02d',
    b = { field = 'monthabbr' },
    date.hour,
    B = { field = 'monthname' },
    date.minute,
    u = { fmt = '%d'  , field = 'dowiso' },
    date.second
    w = { fmt = '%d'  , field = 'dow' },
    )
    d = { fmt = '%02d', field = 'day' },
    else
    m = { fmt = '%02d', field = 'month' },
    time = string.format(' %02d:%02d',
    Y = { fmt = '%04d', field = 'year' },
    date.hour,
    H = { fmt = '%02d', field = 'hour' },
    date.minute
    M = { fmt = '%02d', field = 'minute' },
    )
    S = { fmt = '%02d', field = 'second' },
    j = { fmt = '%03d', field = 'doy' },
    I = { fmt = '%02d', field = 'hour', special = 'hour12' },
    p = { field = 'hour', special = 'am' },
    X = { fmt = '%02d:%02d:%02d', field = 'hour', special = 'hms' },
    ['-d'] = { fmt = '%d', field = 'day' },
    ['-m'] = { fmt = '%d', field = 'month' },
    ['-Y'] = { fmt = '%d', field = 'year' },
    ['-j'] = { fmt = '%d', field = 'doy' },
    }
    options = make_option_table(options or date.options)
    local amopt = options.am
    local eraopt = options.era
    local function replace_code(id)
    local code = codes[id]
    if code then
    local fmt = code.fmt
    local value = date[code.field]
    local special = code.special
    if special then
    if special == 'hour12' then
    value = value % 12
    value = value == 0 and 12 or value
    elseif special == 'hms' then
    return string.format(fmt, value, date.minute, date.second)
    elseif special == 'am' then
    local ap = ({
    ['a.m.'] = { 'a.m.', 'p.m.' },
    ['AM'] = { 'AM', 'PM' },
    ['A.M.'] = { 'A.M.', 'P.M.' },
    })[amopt] or { 'am', 'pm' }
    return value < 12 and ap[1] or ap[2]
    end
    end
    if code.field == 'year' then
    if eraopt == 'BCMINUS' or eraopt == 'BCNEGATIVE' then
    local sign
    if value >= 0 then
    sign = ''
    else
    sign = eraopt == 'BCMINUS' and MINUS or '-'
    value = -value
    end
    return sign .. string.format(fmt, value)
    end
    if value <= 0 then
    value = 1 - value
    end
    end
    return fmt and string.format(fmt, value) or value
    end
    end
    end
    end
    local y = date.year
    local function replace_property(id)
    local sign = ''
    local result = date[id]
    if y < 0 then
    if type(result) == 'string' then
    sign = MINUS
    if id == 'era' and result ~= '' then
    y = -y
    -- Assume era follows a date.
    return '&nbsp;' .. result
    end
    return result
    end
    if type(result) == 'number' then
    return tostring(result)
    end
    if type(result) == 'boolean' then
    return result and '1' or '0'
    end
    -- This occurs, for example, if id is the name of a function.
    return nil
    end
    end
    return string.format('%s%04d-%02d-%02d%s',
    local PERCENT = '\127PERCENT\127'
    sign,
    return (format
    y,
    :gsub('%%%%', PERCENT)
    date.month,
    :gsub('%%{(%w+)}', replace_property)
    date.day,
    :gsub('%%(-?%a)', replace_code)
    time
    :gsub(PERCENT, '%%')
    )
    )
    end
    end
    local function date_text(date, fmt, options)
    -- Return formatted string from given date.
    if not (type(date) == 'table' and date.isvalid) then
    return '(invalid)'
    end
    if type(fmt) ~= 'string' then
    fmt = '%Y-%m-%d'
    if date.hastime then
    if date.second > 0 then
    fmt = fmt .. ' %H:%M:%S'
    else
    fmt = fmt .. ' %H:%M'
    end
    end
    return strftime(date, fmt, options or { era = 'BCMINUS' })
    end
    if fmt:find('%', 1, true) then
    return strftime(date, fmt, options)
    end
    local t = collection()
    for item in fmt:gmatch('%S+') do
    local f
    if item == 'hm' then
    f = '%H:%M'
    elseif item == 'hms' then
    f = '%H:%M:%S'
    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 '(invalid format)'
    end
    t:add(f)
    end
    return strftime(date, t:join(' '), 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 month_number(text)
    local function month_number(text)
    Line 242: Line 388:
    return nil
    return nil
    end
    end
    local era_text = {
    -- options.era = { year<0  , year>0 }
    ['BCMINUS']    = { MINUS  , ''    },
    ['BCNEGATIVE'] = { '-'    , ''    },
    ['BC']        = { 'BC'    , ''    },
    ['B.C.']      = { 'B.C.'  , ''    },
    ['BCE']        = { 'BCE'  , ''    },
    ['B.C.E.']    = { 'B.C.E.', ''    },
    ['AD']        = { 'BC'    , 'AD'  },
    ['A.D.']      = { 'B.C.'  , 'A.D.' },
    ['CE']        = { 'BCE'  , 'CE'  },
    ['C.E.']      = { 'B.C.E.', 'C.E.' },
    }


    -- Metatable for some operations on dates.
    -- Metatable for some operations on dates.
    -- For Lua 5.1, __lt does not work if the metatable is an anonymous table.
    -- For Lua 5.1, __lt does not work if the metatable is an anonymous table.
    local Date  -- forward declaration
    local datemt = {
    local datemt = {
    __eq = function (lhs, rhs)
    __eq = function (lhs, rhs)
    Line 263: Line 424:
    __index = function (self, key)
    __index = function (self, key)
    local value
    local value
    if key == 'jd' or key == 'jdz' then
    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.jd + 1) % 7  -- day-of-week 0=Sun to 6=Sat
    elseif key == 'dowiso' then
    value = (self.jd % 7) + 1  -- ISO day-of-week 1=Mon to 7=Sun
    elseif key == 'doy' then
    local first = Date(self.year, 1, 1, self.calname).jd
    value = self.jd - first + 1  -- day-of-year 1 to 366
    elseif key == 'era' then
    -- Era text from year and options.
    local eraopt = self.options.era
    local sign
    if self.year == 0 then
    sign = (eraopt == 'BCMINUS' or eraopt == 'BCNEGATIVE') and 2 or 1
    else
    sign = self.year > 0 and 2 or 1
    end
    value = era_text[eraopt][sign]
    elseif key == 'gsd' then
    -- GSD = 1 from 00:00:00 to 23:59:59 on 1 January 1 AD Gregorian calendar,
    -- which is JDN = 1721426, and is from jd 1721425.5 to 1721426.49999.
    value = math.floor(self.jd - 1721424.5)
    elseif key == 'jd' or key == 'jdz' then
    local jd, jdz = julian_date(self)
    local jd, jdz = julian_date(self)
    rawset(self, 'jd', jd)
    rawset(self, 'jd', jd)
    rawset(self, 'jdz', jdz)
    rawset(self, 'jdz', jdz)
    return key == 'jd' and jd or jdz
    return key == 'jd' and jd or jdz
    elseif key == 'gsd' then
    -- GSD = 1 from 00:00:00 to 23:59:59 on 1 January 1 AD Gregorian calendar,
    -- which is JDN = 1721426, and is from jd 1721425.5 to 1721426.49999.
    value = math.floor(self.jd - 1721424.5)
    elseif key == 'is_leap_year' then
    elseif key == 'is_leap_year' then
    value = is_leap_year(self.year, self.calname)
    value = is_leap_year(self.year, self.calname)
    elseif key == 'monthabbr' then
    value = month_info[self.month][1]
    elseif key == 'monthname' then
    value = month_info[self.month][2]
    end
    end
    if value ~= nil then
    if value ~= nil then
    Line 294: Line 480:
    Date('04:30:59 1 April 1995', 'julian')
    Date('04:30:59 1 April 1995', 'julian')
    ]]
    ]]
    local function Date(...)
    function Date(...) -- for forward declaration above
    -- Return a table to hold a date assuming a uniform calendar always applies (proleptic).
    -- Return a table to hold a date assuming a uniform calendar always applies (proleptic).
    -- If invalid, return an empty table which is regarded as invalid.
    -- If invalid, return an empty table which is regarded as invalid.
    local calendars = { julian = 'JCAL', Julian = 'JCAL', gregorian = 'GCAL', Gregorian = 'GCAL' }
    local calendars = { julian = 'Julian', gregorian = 'Gregorian' }
    local result = {
    local result = {
    isvalid = false,   -- false avoids __index lookup
    isvalid = false, -- false avoids __index lookup
    calname = 'GCAL',  -- default is Gregorian calendar
    calname = 'Gregorian',  -- default is Gregorian calendar
    hastime = false,   -- true if input sets a time
    hastime = false, -- true if input sets a time
    hour = 0,         -- always set hour/minute/second so don't have to handle nil
    hour = 0, -- always set hour/minute/second so don't have to handle nil
    minute = 0,
    minute = 0,
    second = 0,
    second = 0,
    Line 308: Line 494:
    return days_in_month(self.year, month, self.calname)
    return days_in_month(self.year, month, self.calname)
    end,
    end,
    -- Valid option settings are:
    -- am: 'am', 'a.m.', 'AM', 'A.M.'
    -- era: 'BCMINUS', 'BCNEGATIVE', 'BC', 'B.C.', 'BCE', 'B.C.E.', 'AD', 'A.D.', 'CE', 'C.E.'
    options = { am = 'am', era = 'BC' },
    text = date_text,
    text = date_text,
    }
    }
    Line 315: Line 505:
    for _, v in ipairs({...}) do
    for _, v in ipairs({...}) do
    v = strip_to_nil(v)
    v = strip_to_nil(v)
    local vlower = type(v) == 'string' and v:lower() or nil
    if v == nil then
    if v == nil then
    -- Ignore empty arguments after stripping so modules can directly pass template parameters.
    -- Ignore empty arguments after stripping so modules can directly pass template parameters.
    elseif calendars[v] then
    elseif calendars[vlower] then
    result.calname = calendars[v]
    result.calname = calendars[vlower]
    else
    else
    local num = tonumber(v)
    local num = tonumber(v)
    Line 376: Line 567:
    result.hastime = true
    result.hastime = true
    end
    end
    result.calname = 'GCAL'  -- ignore any given calendar name
    result.calname = 'Gregorian'  -- ignore any given calendar name
    result.isvalid = true
    result.isvalid = true
    elseif argtype == 'setdate' then
    elseif argtype == 'setdate' then
    Line 418: Line 609:
    -- TODO Replace with something using Julian dates?
    -- TODO Replace with something using Julian dates?
    --      Who checks for isvalid()?
    --      Who checks for isvalid()?
    --      Handle calname == 'JCAL'
    --      Handle calname == 'Julian'
    local calname = 'GCAL'  -- TODO fix
    local calname = 'Gregorian'  -- TODO fix
    local isnegative
    local isnegative
    if date2 < date1 then
    if date2 < date1 then

    Revision as of 09:51, 29 February 2016

    Documentation for this module may be created at Module:Date/doc

    -- Date functions for implementing templates and for use by other modules.
    -- I18N and time zones are not supported.
    
    local MINUS = '−'  -- Unicode U+2212 MINUS SIGN
    
    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 = function (self, sep)
    			return table.concat(self, sep)
    		end,
    	}
    end
    
    local function strip_to_nil(text)
    	-- Return nil if text is nil or is an empty string after trimming.
    	-- If text is a non-blank string, return its content after trimming.
    	-- Otherwise return text (convenient when accessed via another module).
    	if type(text) == 'string' then
    		local result = text:match("^%s*(.-)%s*$")
    		if result == '' then
    			return nil
    		end
    		return result
    	end
    	if text == nil then
    		return nil
    	end
    	return text
    end
    
    local function number_name(number, singular, plural, sep)
    	-- Return the given number, converted to a string, with the
    	-- separator (default space) and singular or plural name appended.
    	plural = plural or (singular .. 's')
    	sep = sep or ' '
    	return tostring(number) .. sep .. ((number == 1) and singular or plural)
    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).
    	local month_days = { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }
    	if month == 2 and is_leap_year(year, calname) then
    		return 29
    	end
    	return month_days[month]
    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 = similar, but fractional part is zero at 00:00:00
    	-- 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
    	if not date.isvalid then
    		return 0, 0  -- always return numbers to simplify usage
    	end
    	local floor = math.floor
    	local offset
    	local a = floor((14 - date.month)/12)
    	local y = date.year + 4800 - a
    	if date.calname == '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 date_part = date.day + floor((153*m + 2)/5) + 365*y + offset
    	local time_part, zbias
    	if date.hastime then
    		time_part = (date.hour + (date.minute + date.second / 60) /60) / 24 - 0.5
    		zbias = 0
    	else
    		time_part = 0
    		zbias = -0.5
    	end
    	local jd = date_part + time_part
    	return jd, jd + zbias
    end
    
    local function set_date_from_jd(date)
    	-- Set the fields of table date from its Julian date field.
    	-- 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 floor = math.floor
    	local calname = date.calname
    	local jd = date.jd
    	local limits  -- min/max limits for date ranges −9999-01-01 to 9999-12-31
    	if calname == 'Julian' then
    		limits = { -1931076.5, 5373557.49999 }
    	elseif calname == 'Gregorian' then
    		limits = { -1930999.5, 5373484.49999 }
    	else
    		limits = { 1, 0 }  -- impossible
    	end
    	if not (limits[1] <= jd and jd <= limits[2]) then
    		date.isvalid = false
    		return
    	end
    	date.isvalid = true
    	local jdn = floor(jd)
    	if date.hastime then
    		local time = jd - jdn
    		local hour
    		if time >= 0.5 then
    			jdn = jdn + 1
    			time = time - 0.5
    			hour = 0
    		else
    			hour = 12
    		end
    		time = floor(time * 24 * 3600 + 0.5)  -- number of seconds after hour
    		date.second = time % 60
    		time = floor(time / 60)
    		date.minute = time % 60
    		date.hour = hour + floor(time / 60)
    	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)
    end
    
    local function make_option_table(options)
    	-- If options is a string, return a table with its settings.
    	-- Otherwise return options (it should already be a table).
    	if type(options) == 'string' then
    		-- Example: 'am:AM era:BC'
    		local result = {}
    		for item in options:gmatch('%S+') do
    			local lhs, rhs = item:match('^(%w+):(.*)$')
    			if lhs then
    				result[lhs] = rhs
    			end
    		end
    		return result
    	end
    	return options
    end
    
    local function strftime(date, format, options)
    	-- Return date formatted as a string using codes similar to those
    	-- in the C strftime library function.
    	if not date.isvalid then
    		return '(invalid)'
    	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', field = 'day' },
    		m = { fmt = '%02d', field = 'month' },
    		Y = { fmt = '%04d', field = 'year' },
    		H = { fmt = '%02d', field = 'hour' },
    		M = { fmt = '%02d', field = 'minute' },
    		S = { fmt = '%02d', field = 'second' },
    		j = { fmt = '%03d', field = 'doy' },
    		I = { fmt = '%02d', field = 'hour', special = 'hour12' },
    		p = { field = 'hour', special = 'am' },
    		X = { fmt = '%02d:%02d:%02d', field = 'hour', special = 'hms' },
    		['-d'] = { fmt = '%d', field = 'day' },
    		['-m'] = { fmt = '%d', field = 'month' },
    		['-Y'] = { fmt = '%d', field = 'year' },
    		['-j'] = { fmt = '%d', field = 'doy' },
    	}
    	options = make_option_table(options or date.options)
    	local amopt = options.am
    	local eraopt = options.era
    	local function replace_code(id)
    		local code = codes[id]
    		if code then
    			local fmt = code.fmt
    			local value = date[code.field]
    			local special = code.special
    			if special then
    				if special == 'hour12' then
    					value = value % 12
    					value = value == 0 and 12 or value
    				elseif special == 'hms' then
    					return string.format(fmt, value, date.minute, date.second)
    				elseif special == 'am' then
    					local ap = ({
    						['a.m.'] = { 'a.m.', 'p.m.' },
    						['AM'] = { 'AM', 'PM' },
    						['A.M.'] = { 'A.M.', 'P.M.' },
    					})[amopt] or { 'am', 'pm' }
    					return value < 12 and ap[1] or ap[2]
    				end
    			end
    			if code.field == 'year' then
    				if eraopt == 'BCMINUS' or eraopt == 'BCNEGATIVE' then
    					local sign
    					if value >= 0 then
    						sign = ''
    					else
    						sign = eraopt == 'BCMINUS' and MINUS or '-'
    						value = -value
    					end
    					return sign .. string.format(fmt, value)
    				end
    				if value <= 0 then
    					value = 1 - value
    				end
    			end
    			return fmt and string.format(fmt, value) or value
    		end
    	end
    	local function replace_property(id)
    		local result = date[id]
    		if type(result) == 'string' then
    			if id == 'era' and result ~= '' then
    				-- Assume era follows a date.
    				return '&nbsp;' .. result
    			end
    			return result
    		end
    		if type(result) == 'number' then
    			return tostring(result)
    		end
    		if type(result) == 'boolean' then
    			return result and '1' or '0'
    		end
    		-- This occurs, for example, if id is the name of a function.
    		return nil
    	end
    	local PERCENT = '\127PERCENT\127'
    	return (format
    		:gsub('%%%%', PERCENT)
    		:gsub('%%{(%w+)}', replace_property)
    		:gsub('%%(-?%a)', replace_code)
    		:gsub(PERCENT, '%%')
    	)
    end
    
    local function date_text(date, fmt, options)
    	-- Return formatted string from given date.
    	if not (type(date) == 'table' and date.isvalid) then
    		return '(invalid)'
    	end
    	if type(fmt) ~= 'string' then
    		fmt = '%Y-%m-%d'
    		if date.hastime then
    			if date.second > 0 then
    				fmt = fmt .. ' %H:%M:%S'
    			else
    				fmt = fmt .. ' %H:%M'
    			end
    		end
    		return strftime(date, fmt, options or { era = 'BCMINUS' })
    	end
    	if fmt:find('%', 1, true) then
    		return strftime(date, fmt, options)
    	end
    	local t = collection()
    	for item in fmt:gmatch('%S+') do
    		local f
    		if item == 'hm' then
    			f = '%H:%M'
    		elseif item == 'hms' then
    			f = '%H:%M:%S'
    		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 '(invalid format)'
    		end
    		t:add(f)
    	end
    	return strftime(date, t:join(' '), 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 month_number(text)
    	if type(text) == 'string' then
    		local month_names = {
    			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,
    			oct = 10, october = 10,
    			nov = 11, november = 11,
    			dec = 12, december = 12
    		}
    		return month_names[text:lower()]
    	end
    end
    
    -- A table to get the current year/month/day (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 date_component(named, positional, component)
    	-- Return the first of the two arguments (named like {{example|year=2001}}
    	-- or positional like {{example|2001}}) that is not nil and is not empty.
    	-- If both are nil, return the current date component, if specified.
    	-- This translates empty arguments passed to the template to nil, and
    	-- optionally replaces a nil argument with a value from the current date.
    	named = strip_to_nil(named)
    	if named then
    		return named
    	end
    	positional = strip_to_nil(positional)
    	if positional then
    		return positional
    	end
    	if component then
    		return current[component]
    	end
    	return nil
    end
    
    local era_text = {
    	-- options.era = { year<0  , year>0 }
    	['BCMINUS']    = { MINUS   , ''     },
    	['BCNEGATIVE'] = { '-'     , ''     },
    	['BC']         = { 'BC'    , ''     },
    	['B.C.']       = { 'B.C.'  , ''     },
    	['BCE']        = { 'BCE'   , ''     },
    	['B.C.E.']     = { 'B.C.E.', ''     },
    	['AD']         = { 'BC'    , 'AD'   },
    	['A.D.']       = { 'B.C.'  , 'A.D.' },
    	['CE']         = { 'BCE'   , 'CE'   },
    	['C.E.']       = { 'B.C.E.', 'C.E.' },
    }
    
    -- Metatable for some operations on dates.
    -- For Lua 5.1, __lt does not work if the metatable is an anonymous table.
    local Date  -- forward declaration
    local datemt = {
    	__eq = function (lhs, rhs)
    		-- Return true if dates identify same date/time where, for example,
    		-- (-4712, 1, 1, 'Julian') == (-4713, 11, 24, 'Gregorian').
    		return lhs.isvalid and rhs.isvalid and lhs.jdz == rhs.jdz
    	end,
    	__lt = function (lhs, rhs)
    		-- Return true if lhs < rhs.
    		if not lhs.isvalid then
    			return true
    		end
    		if not rhs.isvalid then
    			return false
    		end
    		return lhs.jdz < rhs.jdz
    	end,
    	__index = function (self, key)
    		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.jd + 1) % 7  -- day-of-week 0=Sun to 6=Sat
    		elseif key == 'dowiso' then
    			value = (self.jd % 7) + 1  -- ISO day-of-week 1=Mon to 7=Sun
    		elseif key == 'doy' then
    			local first = Date(self.year, 1, 1, self.calname).jd
    			value = self.jd - first + 1  -- day-of-year 1 to 366
    		elseif key == 'era' then
    			-- Era text from year and options.
    			local eraopt = self.options.era
    			local sign
    			if self.year == 0 then
    				sign = (eraopt == 'BCMINUS' or eraopt == 'BCNEGATIVE') and 2 or 1
    			else
    				sign = self.year > 0 and 2 or 1
    			end
    			value = era_text[eraopt][sign]
    		elseif key == 'gsd' then
    			-- GSD = 1 from 00:00:00 to 23:59:59 on 1 January 1 AD Gregorian calendar,
    			-- which is JDN = 1721426, and is from jd 1721425.5 to 1721426.49999.
    			value = math.floor(self.jd - 1721424.5)
    		elseif key == 'jd' or key == 'jdz' then
    			local jd, jdz = julian_date(self)
    			rawset(self, 'jd', jd)
    			rawset(self, 'jdz', jdz)
    			return key == 'jd' and jd or jdz
    		elseif key == 'is_leap_year' then
    			value = is_leap_year(self.year, self.calname)
    		elseif key == 'monthabbr' then
    			value = month_info[self.month][1]
    		elseif key == 'monthname' then
    			value = month_info[self.month][2]
    		end
    		if value ~= nil then
    			rawset(self, key, value)
    			return value
    		end
    	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 "." text output includes H:M:S
    Date('currentdate')
    Date('currentdatetime')
    LATER: Following are not yet implemented:
    Date('currentdate', H, M, S) 	    current date with given time
    Date('1 April 1995', 'julian') 	    parse date from text
    Date('1 April 1995 AD', 'julian')   AD, CE, BC, BCE (using one of these sets a flag to do same for output)
    Date('04:30:59 1 April 1995', 'julian')
    ]]
    function Date(...)  -- for forward declaration above
    	-- Return a table to hold a date assuming a uniform calendar always applies (proleptic).
    	-- If invalid, return an empty table which is regarded as invalid.
    	local calendars = { julian = 'Julian', gregorian = 'Gregorian' }
    	local result = {
    		isvalid = false,  -- false avoids __index lookup
    		calname = '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,
    		month_days = function (self, month)
    			return days_in_month(self.year, month, self.calname)
    		end,
    		-- Valid option settings are:
    		-- am: 'am', 'a.m.', 'AM', 'A.M.'
    		-- era: 'BCMINUS', 'BCNEGATIVE', 'BC', 'B.C.', 'BCE', 'B.C.E.', 'AD', 'A.D.', 'CE', 'C.E.'
    		options = { am = 'am', era = 'BC' },
    		text = date_text,
    	}
    	local numbers = collection()
    	local datetext
    	local argtype
    	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
    			result.calname = calendars[vlower]
    		else
    			local num = tonumber(v)
    			if not num and argtype == 'setdate' and numbers.n == 1 then
    				num = month_number(v)
    			end
    			if num then
    				if not argtype then
    					argtype = 'setdate'
    				end
    				numbers:add(num)
    				if argtype == 'juliandate' then
    					if type(v) == 'string' then
    						if v:find('.', 1, true) then
    							result.hastime = true
    						end
    					elseif num ~= math.floor(num) then
    						-- The given value was a number. The time will be used
    						-- if the fractional part is nonzero.
    						result.hastime = true
    					end
    				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 numbers.n > 0 then
    			return {}
    		end
    		-- TODO Parse datetext to extract y,m,d,H,M,S.
    	elseif argtype == 'juliandate' then
    		if numbers.n == 1 then
    			result.jd = numbers[1]
    			set_date_from_jd(result)
    		else
    			return {}
    		end
    	elseif argtype == 'currentdate' or argtype == 'currentdatetime' then
    		result.year = current.year
    		result.month = current.month
    		result.day = current.day
    		if argtype == 'currentdatetime' then
    			result.hour = current.hour
    			result.minute = current.minute
    			result.second = current.second
    			result.hastime = true
    		end
    		result.calname = 'Gregorian'  -- ignore any given calendar name
    		result.isvalid = true
    	elseif argtype == 'setdate' then
    		if not (3 <= numbers.n and numbers.n <= 6) then
    			return {}
    		end
    		local y, m, d = numbers[1], numbers[2], numbers[3]
    		if not (-9999 <= y and y <= 9999 and 1 <= m and m <= 12 and
    					1 <= d and d <= days_in_month(y, m, result.calname)) then
    			return {}
    		end
    		local H = numbers[4]
    		if H then
    			result.hastime = true
    		else
    			H = 0
    		end
    		local M = numbers[5] or 0
    		local S = numbers[6] or 0
    		if not (0 <= H and H <= 23 and
    				0 <= M and M <= 59 and
    				0 <= S and S <= 59) then
    			return {}
    		end
    		result.year = y    -- -9999 to 9999; '1 BC' → year = 0; 'n BC' → year = 1 - n
    		result.month = m   -- 1 to 12
    		result.day = d     -- 1 to 31
    		result.hour = H    -- 0 to 59
    		result.minute = M  -- 0 to 59
    		result.second = S  -- 0 to 59
    		result.isvalid = true
    	else
    		return {}
    	end
    	return setmetatable(result, datemt)
    end
    
    local function DateDiff(date1, date2)
    	-- Return a table to with the difference between the two given dates.
    	-- Difference is negative if the second date is older than the first.
    	-- TODO Replace with something using Julian dates?
    	--      Who checks for isvalid()?
    	--      Handle calname == 'Julian'
    	local calname = 'Gregorian'  -- TODO fix
    	local isnegative
    	if date2 < date1 then
    		isnegative = true
    		date1, date2 = date2, date1
    	end
    	-- It is known that date1 <= date2.
    	local y1, m1 = date1.year, date1.month
    	local y2, m2 = date2.year, date2.month
    	local years, months, days = y2 - y1, m2 - m1, date2.day - date1.day
    	if days < 0 then
    		days = days + days_in_month(y1, m1, calname)
    		months = months - 1
    	end
    	if months < 0 then
    		months = months + 12
    		years = years - 1
    	end
    	return {
    		years = years,
    		months = months,
    		days = days,
    		isnegative = isnegative,
    		age_ym = function (self)
    			-- Return text specifying difference in years, months.
    			local sign = self.isnegative and MINUS or ''
    			local mtext = number_name(self.months, 'month')
    			local result
    			if self.years > 0 then
    				local ytext = number_name(self.years, 'year')
    				if self.months == 0 then
    					result = ytext
    				else
    					result = ytext .. ',&nbsp;' .. mtext
    				end
    			else
    				if self.months == 0 then
    					sign = ''
    				end
    				result = mtext
    			end
    			return sign .. result
    		end,
    	}
    end
    
    local function message(msg, nocat)
    	-- Return formatted message text for an error.
    	-- Can append "#FormattingError" to URL of a page with a problem to find it.
    	local anchor = '<span id="FormattingError" />'
    	local category
    	if not nocat and mw.title.getCurrentTitle():inNamespaces(0, 10) then
    		-- Category only in namespaces: 0=article, 10=template.
    		category = '[[Category:Age error]]'
    	else
    		category = ''
    	end
    	return anchor ..
    		'<strong class="error">Error: ' ..
    		msg ..
    		'</strong>' ..
    		category .. '\n'
    end
    
    local function age_days(frame)
    	-- Return age in days between two given dates, or
    	-- between given date and current date.
    	-- This code implements the logic in [[Template:Age in days]].
    	-- Like {{Age in days}}, a missing argument is replaced from the current
    	-- date, so can get a bizarre mixture of specified/current y/m/d.
    	local args = frame:getParent().args
    	local date1 = Date(
    		date_component(args.year1 , args[1], 'year' ),
    		date_component(args.month1, args[2], 'month'),
    		date_component(args.day1  , args[3], 'day'  )
    	)
    	local date2 = Date(
    		date_component(args.year2 , args[4], 'year' ),
    		date_component(args.month2, args[5], 'month'),
    		date_component(args.day2  , args[6], 'day'  )
    	)
    	if not (date1.isvalid and date2.isvalid) then
    		return message('Need valid year, month, day')
    	end
    	local sign = ''
    	local result = date2.jd - date1.jd
    	if result < 0 then
    		sign = MINUS
    		result = -result
    	end
    	return sign .. tostring(result)
    end
    
    local function age_ym(frame)
    	-- Return age in years and months between two given dates, or
    	-- between given date and current date.
    	local args = frame:getParent().args
    	local fields = {}
    	for i = 1, 6 do
    		fields[i] = strip_to_nil(args[i])
    	end
    	local date1, date2
    	if fields[1] and fields[2] and fields[3] then
    		date1 = Date(fields[1], fields[2], fields[3])
    	end
    	if not (date1 and date1.isvalid) then
    		return message('Need valid year, month, day')
    	end
    	if fields[4] and fields[5] and fields[6] then
    		date2 = Date(fields[4], fields[5], fields[6])
    		if not date2.isvalid then
    			return message('Second date should be year, month, day')
    		end
    	else
    		date2 = Date('currentdate')
    	end
    	return DateDiff(date1, date2):age_ym()
    end
    
    local function gsd_ymd(frame)
    	-- Return Gregorian serial date of the given date, or the current date.
    	-- Like {{Gregorian serial date}}, a missing argument is replaced from the
    	-- current date, so can get a bizarre mixture of specified/current y/m/d.
    	-- This also accepts positional arguments, although the original template does not.
    	-- The returned value is negative for dates before 1 January 1 AD despite
    	-- the fact that GSD is not defined for earlier dates.
    	local args = frame:getParent().args
    	local date = Date(
    		date_component(args.year , args[1], 'year' ),
    		date_component(args.month, args[2], 'month'),
    		date_component(args.day  , args[3], 'day'  )
    	)
    	if date.isvalid then
    		return tostring(date.gsd)
    	end
    	return message('Need valid year, month, day')
    end
    
    local function ymd_from_jd(frame)
    	-- Return formatted date from a Julian date.
    	-- The result is y-m-d or y-m-d H:M:S if input includes a fraction.
    	-- The word 'Julian' is accepted for the Julian calendar.
    	local args = frame:getParent().args
    	local date = Date('juliandate', args[1], args[2])
    	if date.isvalid then
    		return date:text()
    	end
    	return message('Need valid Julian date number')
    end
    
    local function ymd_to_jd(frame)
    	-- Return Julian date (a number) from a date (y-m-d), or datetime (y-m-d H:M:S),
    	-- or the current date ('currentdate') or current datetime ('currentdatetime').
    	-- The word 'Julian' is accepted for the Julian calendar.
    	local args = frame:getParent().args
    	local date = Date(args[1], args[2], args[3], args[4], args[5], args[6], args[7])
    	if date.isvalid then
    		return tostring(date.jd)
    	end
    	return message('Need valid year/month/day or "currentdate"')
    end
    
    return {
    	age_days = age_days,
    	age_ym = age_ym,
    	_Date = Date,
    	days_in_month = days_in_month,
    	gsd = gsd_ymd,
    	JULIANDAY = ymd_to_jd,
    	ymd_from_jd = ymd_from_jd,
    	ymd_to_jd = ymd_to_jd,
    }