```{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-}
-- |
-- Module    : Statistics.Distribution.Uniform
-- Copyright : (c) 2011 Aleksey Khudyakov
--
-- Maintainer  : bos@serpentine.com
-- Stability   : experimental
-- Portability : portable
--
-- Variate distributed uniformly in the interval.
module Statistics.Distribution.Uniform
(
UniformDistribution
-- * Constructors
, uniformDistr
-- ** Accessors
, uniformA
, uniformB
) where

import Data.Binary (Binary)
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D
import qualified System.Random.MWC       as MWC
import Data.Binary (put, get)
import Control.Applicative ((<\$>), (<*>))

-- | Uniform distribution from A to B
data UniformDistribution = UniformDistribution {
uniformA :: {-# UNPACK #-} !Double -- ^ Low boundary of distribution
, uniformB :: {-# UNPACK #-} !Double -- ^ Upper boundary of distribution
} deriving (Eq, Read, Show, Typeable, Data, Generic)

instance Binary UniformDistribution where
put (UniformDistribution x y) = put x >> put y
get = UniformDistribution <\$> get <*> get

-- | Create uniform distribution.
uniformDistr :: Double -> Double -> UniformDistribution
uniformDistr a b
| b < a     = uniformDistr b a
| a < b     = UniformDistribution a b
| otherwise = error "Statistics.Distribution.Uniform.uniform: wrong parameters"
-- NOTE: failure is in default branch to guard againist NaNs.

instance D.Distribution UniformDistribution where
cumulative (UniformDistribution a b) x
| x < a     = 0
| x > b     = 1
| otherwise = (x - a) / (b - a)

instance D.ContDistr UniformDistribution where
density (UniformDistribution a b) x
| x < a     = 0
| x > b     = 0
| otherwise = 1 / (b - a)
quantile (UniformDistribution a b) p
| p >= 0 && p <= 1 = a + (b - a) * p
| otherwise        =
error \$ "Statistics.Distribution.Uniform.quantile: p must be in [0,1] range. Got: "++show p

instance D.Mean UniformDistribution where
mean (UniformDistribution a b) = 0.5 * (a + b)

instance D.Variance UniformDistribution where
-- NOTE: 1/sqrt 12 is not constant folded (#4101) so it's written as
--       numerical constant. (Also FIXME!)
stdDev   (UniformDistribution a b) = 0.2886751345948129 * (b - a)
variance (UniformDistribution a b) = d * d / 12 where d = b - a

instance D.MaybeMean UniformDistribution where
maybeMean = Just . D.mean

instance D.MaybeVariance UniformDistribution where
maybeStdDev   = Just . D.stdDev

instance D.Entropy UniformDistribution where
entropy (UniformDistribution a b) = log (b - a)

instance D.MaybeEntropy UniformDistribution where
maybeEntropy = Just . D.entropy

instance D.ContGen UniformDistribution where
genContVar (UniformDistribution a b) gen = MWC.uniformR (a,b) gen
```