```module Data.Time.Calendar.MonthDay
(
monthAndDayToDayOfYear,monthAndDayToDayOfYearValid,dayOfYearToMonthAndDay,monthLength
) where

import Data.Time.Calendar.Private

-- | convert month and day in the Gregorian or Julian calendars to day of year.
-- First arg is leap year flag
monthAndDayToDayOfYear :: Bool -> Int -> Int -> Int
monthAndDayToDayOfYear isLeap month day = (div (367 * month'' - 362) 12) + k + day' where
month' = clip 1 12 month
day' = fromIntegral (clip 1 (monthLength' isLeap month') day)
month'' = fromIntegral month'
k = if month' <= 2 then 0 else if isLeap then -1 else -2

-- | convert month and day in the Gregorian or Julian calendars to day of year.
-- First arg is leap year flag
monthAndDayToDayOfYearValid :: Bool -> Int -> Int -> Maybe Int
monthAndDayToDayOfYearValid isLeap month day = do
month' <- clipValid 1 12 month
day' <- clipValid 1 (monthLength' isLeap month') day
let
day'' = fromIntegral day'
month'' = fromIntegral month'
k = if month' <= 2 then 0 else if isLeap then -1 else -2
return ((div (367 * month'' - 362) 12) + k + day'')

-- | convert day of year in the Gregorian or Julian calendars to month and day.
-- First arg is leap year flag
dayOfYearToMonthAndDay :: Bool -> Int -> (Int,Int)
dayOfYearToMonthAndDay isLeap yd = findMonthDay (monthLengths isLeap) (clip 1 (if isLeap then 366 else 365) yd)

findMonthDay :: [Int] -> Int -> (Int,Int)
findMonthDay (n:ns) yd | yd > n = (\(m,d) -> (m + 1,d)) (findMonthDay ns (yd - n))
findMonthDay _ yd = (1,yd)

-- | the length of a given month in the Gregorian or Julian calendars.
-- First arg is leap year flag
monthLength :: Bool -> Int -> Int
monthLength isLeap month' = monthLength' isLeap (clip 1 12 month')

monthLength' :: Bool -> Int -> Int
monthLength' isLeap month' = (monthLengths isLeap) !! (month' - 1)

monthLengths :: Bool -> [Int]
monthLengths isleap =
[31,if isleap then 29 else 28,31,30,31,30,31,31,30,31,30,31]
--J        F                   M  A  M  J  J  A  S  O  N  D
```