module System.Random.MWC.Monad ( -- * Random monad
                                 Rand
                               , RandIO
                               , asRandIO
                               , RandST
                               , asRandST
                               , Seed
                               , runRand
                               , runWithSeed
                               , runWithVector
                               , runWithSystemRandom
                                 -- * Random numbers generation
                               , toRand
                               , uniform
                               , uniformR
                               , standard
                               , normal
                                 -- * Seed management
                               , save
                               ) where

import Control.Applicative
import Control.Monad           (ap)
import Control.Monad.ST        (ST)
import Control.Monad.Primitive (PrimMonad, PrimState)

import Data.Vector.Unboxed (Vector)
import Data.Word           (Word32)

import qualified System.Random.MWC as MWC
import           System.Random.MWC   (Gen,Variate,Seed)

----------------------------------------------------------------

-- | Random monad for mwc-random package
newtype Rand m a = Rand {
  -- | Run random monad
  runRand :: Gen (PrimState m) -> m a
  }

-- | Type synonim for ST-based Rand monad
type RandST s a = Rand (ST s) a

-- | Fix type of monad to ST
asRandST :: RandST s a -> RandST s a
asRandST = id
{-# INLINE asRandST #-}

-- | Type synonim for IO-based Rand monad
type RandIO a   = Rand IO a

-- | Fix type of monad to IO
asRandIO :: RandIO a -> RandIO a
asRandIO = id
{-# INLINE asRandIO #-}

-- | Run monad using fixed seed
runWithCreate :: PrimMonad m => Rand m a -> m a
runWithCreate m = runRand m =<< MWC.create
{-# INLINE runWithCreate #-}

-- | By creating seed from vector of values
runWithVector :: PrimMonad m => Rand m a -> Vector Word32 -> m a
runWithVector m v = runRand m =<< MWC.initialize v
{-# INLINE runWithVector #-}

-- | Run monad using seed
runWithSeed :: PrimMonad m => Seed -> Rand m a -> m a
runWithSeed seed m = runRand m =<< MWC.restore seed
{-# INLINE runWithSeed #-}

-- | Run monad using system random
runWithSystemRandom :: PrimMonad m => Rand m a -> IO a
runWithSystemRandom = MWC.withSystemRandom . runRand
{-# INLINE runWithSystemRandom #-}

instance PrimMonad m => Functor (Rand m) where
  fmap f (Rand rnd) = Rand $ \g -> (return . f) =<< (rnd g)
  {-# INLINE fmap #-}

instance PrimMonad m => Monad (Rand m) where
  return x         = Rand (\_ -> return x)
  (Rand rnd) >>= f = Rand $ \g -> (\x -> runRand (f x) g) =<< rnd g
  {-# INLINE return #-}
  {-# INLINE (>>=)  #-}

instance (PrimMonad m) => Applicative (Rand m) where
  pure  = return
  (<*>) = ap
  {-# INLINE pure  #-}
  {-# INLINE (<*>) #-}

----------------------------------------------------------------

-- | Convert function to Rand monad
toRand :: PrimMonad m => (Gen (PrimState m) -> m a) -> Rand m a
toRand = Rand
{-# INLINE toRand #-}

-- | Uniformly distributed values
uniform :: (PrimMonad m, Variate a) => Rand m a
uniform = Rand MWC.uniform
{-# INLINE uniform #-}

-- | Uniformly distributed values in range
uniformR :: (PrimMonad m, Variate a) => (a,a) -> Rand m a
uniformR rng = Rand (MWC.uniformR rng)
{-# INLINE uniformR #-}

-- | Normally distributed variables with mean 0 and 1 standard deviation
standard :: PrimMonad m => Rand m Double
standard = Rand MWC.normal
{-# INLINE normal #-}

-- | Normally distributed variable
normal :: PrimMonad m => 
          Double                -- Mean
       -> Double                -- Variance
       -> Rand m Double
normal m s = (+ m) . (* s) <$> standard
{-# INLINE standard #-}

----------------------------------------------------------------

-- | Save current seed for future reuse
save :: PrimMonad m => Rand m Seed
save = Rand MWC.save