```module Data.Time.Calendar.Julian
(
module Data.Time.Calendar.JulianYearDay,

toJulian,fromJulian,showJulian,julianMonthLength,

-- calendrical arithmetic
-- e.g. "one month after March 31st"
) where

import Data.Time.Calendar.MonthDay
import Data.Time.Calendar.JulianYearDay
import Data.Time.Calendar.Days
import Data.Time.Calendar.Private

-- | convert to proleptic Julian calendar. First element of result is year, second month number (1-12), third day (1-31).
toJulian :: Day -> (Integer,Int,Int)
toJulian date = (year,month,day) where
(year,yd) = toJulianYearAndDay date
(month,day) = dayOfYearToMonthAndDay (isJulianLeapYear year) yd

-- | convert from proleptic Julian calendar. First argument is year, second month number (1-12), third day (1-31).
-- Invalid values will be clipped to the correct range, month first, then day.
fromJulian :: Integer -> Int -> Int -> Day
fromJulian year month day = fromJulianYearAndDay year (monthAndDayToDayOfYear (isJulianLeapYear year) month day)

-- | show in ISO 8601 format (yyyy-mm-dd)
showJulian :: Day -> String
showJulian date = (show4 y) ++ "-" ++ (show2 m) ++ "-" ++ (show2 d) where
(y,m,d) = toJulian date

-- | The number of days in a given month according to the proleptic Julian calendar. First argument is year, second is month.
julianMonthLength :: Integer -> Int -> Int
julianMonthLength year = monthLength (isJulianLeapYear year)

rolloverMonths :: (Integer,Integer) -> (Integer,Int)
rolloverMonths (y,m) = (y + (div (m - 1) 12),fromIntegral (mod (m - 1) 12) + 1)

addJulianMonths :: Integer -> Day -> (Integer,Int,Int)
addJulianMonths n day = (y',m',d) where
(y,m,d) = toJulian day
(y',m') = rolloverMonths (y,fromIntegral m + n)

-- | Add months, with days past the last day of the month clipped to the last day.
-- For instance, 2005-01-30 + 1 month = 2005-02-28.
addJulianMonthsClip :: Integer -> Day -> Day
addJulianMonthsClip n day = fromJulian y m d where

-- | Add months, with days past the last day of the month rolling over to the next month.
-- For instance, 2005-01-30 + 1 month = 2005-03-02.
addJulianMonthsRollOver :: Integer -> Day -> Day
addJulianMonthsRollOver n day = addDays (fromIntegral d - 1) (fromJulian y m 1) where