local strformat = string.format
local floor = math.floor
local function idiv ( n , d )
	return floor ( n / d )
end


local mon_lengths = { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }
-- Number of days in year until start of month; not corrected for leap years
local months_to_days_cumulative = { 0 }
for i = 2, 12 do
	months_to_days_cumulative [ i ] = months_to_days_cumulative [ i-1 ] + mon_lengths [ i-1 ]
end

local function is_leap ( y )
	return (y % 4) == 0 and (y % 100) ~= 0 or (y % 400) == 0
end

local function year_length ( y )
	return is_leap ( y ) and 366 or 365
end

local function month_length ( m , y )
	if m == 2 then
		return is_leap ( y ) and 29 or 28
	else
		return mon_lengths [ m ]
	end
end

local function leap_years_since ( year )
	return idiv ( year , 4 ) - idiv ( year , 100 ) + idiv ( year , 400 )
end

local function doomsday ( year )
	return ( 3 -- Tuesday
		- 1 + year + leap_years_since ( year ) )
		% 7 + 1
end
local doomsday_cache = setmetatable ( { } , {
	__index = function ( cache , year )
		local d = doomsday ( year )
		cache [ year ] = d
		return d
	end ;
} )

local function day_of_year ( day , month , year )
	local yday = months_to_days_cumulative [ month ]
	if month > 2 and is_leap ( year ) then
		yday = yday + 1
	end
	return yday + day
end

local function day_of_week ( yday , year )
	return ( yday - doomsday_cache [ year ] - 1 ) % 7 + 1
end

local function increment ( tens , units , base )
	if units >= base then
		tens  = tens + idiv ( units , base )
		units = units % base
	elseif units < 0 then
		tens  = tens - 1 + idiv ( -units , base )
		units = base - ( -units % base )
	end
	return tens , units
end

-- Modify parameters so they all fit within the "normal" range
local function normalise ( year , month , day , hour , min , sec )
	min  , sec  = increment ( min  , sec  , 60 ) -- TODO: consider leap seconds?
	hour , min  = increment ( hour , min  , 60 )
	day  , hour = increment ( day  , hour , 24 )

	while day <= 0 do
		year = year - 1
		day  = day + year_length ( year )
	end

	-- Lua months start from 1, need -1 and +1 around this increment
	month = month - 1
	year , month = increment ( year , month , 12 )
	month = month + 1

	-- This could potentially be slow if `day` is very large
	while true do
		local i = month_length ( month , year )
		if day <= i then break end
		day = day - i
		month = month + 1
		if month > 12 then
			month = 1
			year = year + 1
		end
	end

	return year , month , day , hour , min , sec
end

local leap_years_since_1970 = leap_years_since ( 1970 )
local function timestamp ( year , month , day , hour , min , sec )
	year , month , day , hour , min , sec = normalise ( year , month , day , hour , min , sec )

	local days_since_epoch = day_of_year ( day , month , year )
		+ 365 * ( year - 1970 )
		-- Each leap year adds one day
		+ ( leap_years_since ( year - 1 ) - leap_years_since_1970 ) - 1

	return days_since_epoch * (60*60*24)
		+ hour  * (60*60)
		+ min   * 60
		+ sec
end


local timetable_methods = { }

function timetable_methods:unpack ( )
	return assert ( self.year  , "year required" ) ,
		assert ( self.month , "month required" ) ,
		assert ( self.day   , "day required" ) ,
		self.hour or 12 ,
		self.min  or 0 ,
		self.sec  or 0 ,
		self.yday ,
		self.wday
end

function timetable_methods:normalise ( )
	local year , month , day
	year , month , day , self.hour , self.min , self.sec = normalise ( self:unpack ( ) )

	self.day   = day
	self.month = month
	self.year  = year

	local yday = day_of_year ( day , month , year )
	local wday = day_of_week ( yday , year )

	self.yday = yday
	self.wday = wday

	return self
end
timetable_methods.normalize = timetable_methods.normalise -- American English

function timetable_methods:timestamp ( )
	return timestamp ( self:unpack ( ) )
end

function timetable_methods:rfc_3339 ( )
	-- %06.4g gives 3 (=6-4+1) digits after decimal
	return strformat ( "%04u-%02u-%02uT%02u:%02u:%06.4g" , self:unpack ( ) )
end

local timetable_mt

local function coerce_arg ( t )
	if getmetatable ( t ) == timetable_mt then
		return t:timestamp ( )
	end
	return t
end

timetable_mt = {
	__index    = timetable_methods ;
	__tostring = timetable_methods.rfc_3339 ;
	__eq = function ( a , b )
		return coerce_arg ( a ) == coerce_arg ( b )
	end ;
	__lt = function ( a , b )
		return coerce_arg ( a ) < coerce_arg ( b )
	end ;
}

local function cast_timetable ( tm )
	return setmetatable ( tm , timetable_mt )
end

local function new_timetable ( year , month , day , hour , min , sec , yday , wday )
	return cast_timetable {
		year  = year ;
		month = month ;
		day   = day ;
		hour  = hour ;
		min   = min ;
		sec   = sec ;
		yday  = yday ;
		wday  = wday ;
	}
end

function timetable_methods:clone ( )
	return new_timetable ( self:unpack ( ) )
end

local function new_from_timestamp ( ts )
	return new_timetable ( 1970 , 1 , 1 , 0 , 0 , ts )
end

return {
	doomsday  = doomsday ;
	normalise = normalise ;
	timestamp = timestamp ;

	new = new_timetable ;
	new_from_timestamp = new_from_timestamp ;
	cast = cast_timetable ;
	timetable_mt = timetable_mt ;
}