```{-# OPTIONS -Wall -Werror #-}

-- #hide
module Data.Time.Clock.Scale
(
-- * Universal Time
-- | Time as measured by the earth.
UniversalTime(..),

-- * Absolute intervals
DiffTime,
secondsToDiffTime, picosecondsToDiffTime
) where

import Data.Ratio ((%))
import Data.Fixed

-- | The Modified Julian Date is the day with the fraction of the day, measured from UT midnight.
-- It's used to represent UT1, which is time as measured by the earth's rotation, adjusted for various wobbles.
newtype UniversalTime = ModJulianDate {getModJulianDate :: Rational} deriving (Eq,Ord)

-- | This is a length of time, as measured by a clock.
-- Conversion functions will treat it as seconds.
-- It has an accuracy of 10^-12 s.
newtype DiffTime = MkDiffTime Pico deriving (Eq,Ord)

-- necessary because H98 doesn't have "cunning newtype" derivation
instance Enum DiffTime where
succ (MkDiffTime a) = MkDiffTime (succ a)
pred (MkDiffTime a) = MkDiffTime (pred a)
toEnum = MkDiffTime . toEnum
enumFrom (MkDiffTime a) = fmap MkDiffTime (enumFrom a)
enumFromThen (MkDiffTime a) (MkDiffTime b) = fmap MkDiffTime (enumFromThen a b)
enumFromTo (MkDiffTime a) (MkDiffTime b) = fmap MkDiffTime (enumFromTo a b)
enumFromThenTo (MkDiffTime a) (MkDiffTime b) (MkDiffTime c) = fmap MkDiffTime (enumFromThenTo a b c)

instance Show DiffTime where
show (MkDiffTime t) = (showFixed True t) ++ "s"

-- necessary because H98 doesn't have "cunning newtype" derivation
instance Num DiffTime where
(MkDiffTime a) + (MkDiffTime b) = MkDiffTime (a + b)
(MkDiffTime a) - (MkDiffTime b) = MkDiffTime (a - b)
(MkDiffTime a) * (MkDiffTime b) = MkDiffTime (a * b)
negate (MkDiffTime a) = MkDiffTime (negate a)
abs (MkDiffTime a) = MkDiffTime (abs a)
signum (MkDiffTime a) = MkDiffTime (signum a)
fromInteger i = MkDiffTime (fromInteger i)

-- necessary because H98 doesn't have "cunning newtype" derivation
instance Real DiffTime where
toRational (MkDiffTime a) = toRational a

-- necessary because H98 doesn't have "cunning newtype" derivation
instance Fractional DiffTime where
(MkDiffTime a) / (MkDiffTime b) = MkDiffTime (a / b)
recip (MkDiffTime a) = MkDiffTime (recip a)
fromRational r = MkDiffTime (fromRational r)

-- | Create a 'DiffTime' which represents an integral number of seconds.
secondsToDiffTime :: Integer -> DiffTime
secondsToDiffTime = fromInteger

-- | Create a 'DiffTime' from a number of picoseconds.
picosecondsToDiffTime :: Integer -> DiffTime
picosecondsToDiffTime x = fromRational (x % 1000000000000)
```