{-# LANGUAGE ScopedTypeVariables, TypeFamilies, DataKinds, FlexibleContexts, DataKinds, DeriveDataTypeable #-}

-- | Signed, fixed sized numbers.
--
-- Copyright: (c) 2009 University of Kansas
-- License: BSD3
--
-- Maintainer: Andy Gill <andygill@ku.edu>
-- Stability: unstable
-- Portability: ghc

module Data.Sized.Signed
	( Signed
	, toVector
	, fromVector
	,           S2,  S3,  S4,  S5,  S6,  S7,  S8,  S9
	, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19
	, S20, S21, S22, S23, S24, S25, S26, S27, S28, S29
	, S30, S31, S32
	) where

import Data.Array.IArray(elems, (!))
import Data.Sized.Matrix as M
import Data.Sized.Fin
import Data.Bits
import Data.Typeable

newtype Signed (ix :: Nat) = Signed Integer
    deriving (Eq, Ord, Typeable)

-- 'toVector' turns a sized 'Signed' value into a 'Vector' of 'Bool's.
toVector :: forall ix . (SingI ix) => Signed ix -> Vector ix Bool
toVector (Signed v) = matrix $ take (fromIntegral $ fromSing (sing :: Sing ix)) $ map odd $ iterate (`div` 2) v

-- 'fromVector' turns a 'Vector' of 'Bool's into a sized 'Signed' value.
fromVector :: (SingI ix) => Vector ix Bool -> Signed ix
fromVector m = mkSigned $
	  sum [ n
	      | (n,b) <- zip (iterate (* 2) 1)
			      (elems m)
	      , b
	      ]
--
mkSigned :: forall ix . (SingI ix) => Integer -> Signed ix
mkSigned v = res
    where sz' = 2 ^ bitCount
          bitCount :: Integer
	  bitCount =  fromIntegral (fromNat (sing :: Sing ix) - 1)
	  res = case divMod v sz' of
	  	  (s,v') | even s    -> Signed v'
		         | otherwise -> Signed (v' - sz')

instance (SingI ix) => Show (Signed ix) where
	show (Signed a) = show a

instance (SingI ix) => Read (Signed ix) where
	readsPrec i str = [ (mkSigned a,r) | (a,r) <- readsPrec i str ]

instance (SingI ix) => Integral (Signed ix) where
  	toInteger (Signed m) = m
	quotRem (Signed a) (Signed b) =
		case quotRem a b of
		   (q,r) -> (mkSigned q,mkSigned r)

instance (SingI ix) => Num (Signed ix) where
	(Signed a) + (Signed b) = mkSigned $ a + b
	(Signed a) - (Signed b) = mkSigned $ a - b
	(Signed a) * (Signed b) = mkSigned $ a * b
	abs (Signed n) = mkSigned $ abs n
	signum (Signed n) = mkSigned $ signum n
	fromInteger n = mkSigned n

instance (SingI ix) => Real (Signed ix) where
	toRational (Signed n) = toRational n

instance (SingI ix) => Enum (Signed ix) where
	fromEnum (Signed n) = fromEnum n
	toEnum n = mkSigned (toInteger n)

instance (SingI ix) => Bits (Signed ix) where
	bitSizeMaybe = return . finiteBitSize
        bitSize = finiteBitSize
	complement (Signed v) = Signed (complement v)
	isSigned _ = True
	a `xor` b = fromVector (M.zipWith (/=) (toVector a) (toVector b))
	a .|. b = fromVector (M.zipWith (||) (toVector a) (toVector b))
	a .&. b = fromVector (M.zipWith (&&) (toVector a) (toVector b))
	shiftL (Signed v) i = mkSigned (v * (2 ^ i))
	shiftR (Signed v) i = mkSigned (v `div` (2 ^ i))
 	rotate v i = fromVector (forAll $ \ ix -> m ! (fromIntegral ((fromIntegral ix - i) `mod` mLeng)))
		where m = toVector v
                      mLeng = size $ M.zeroOf m
        testBit u idx = toVector u ! (fromIntegral idx)
        -- new is 7.6?
        bit   i  = fromVector (forAll $ \ ix -> if ix == fromIntegral i then True else False)
        popCount n = sum $ fmap (\ b -> if b then 1 else 0) $ elems $ toVector n

instance (SingI ix) => FiniteBits (Signed ix) where
	finiteBitSize _ = fromIntegral (fromNat (sing :: Sing ix))

instance forall ix . (SingI ix) => Bounded (Signed ix) where
	minBound = Signed (- maxMagnitude)
            where maxMagnitude = 2 ^ (fromNat (sing :: Sing ix) - 1)
        maxBound = Signed (maxMagnitude - 1)
            where maxMagnitude = 2 ^ (fromNat (sing :: Sing ix) - 1)


type S2 = Signed 2
type S3 = Signed 3
type S4 = Signed 4
type S5 = Signed 5
type S6 = Signed 6
type S7 = Signed 7
type S8 = Signed 8
type S9 = Signed 9
type S10 = Signed 10
type S11 = Signed 11
type S12 = Signed 12
type S13 = Signed 13
type S14 = Signed 14
type S15 = Signed 15
type S16 = Signed 16
type S17 = Signed 17
type S18 = Signed 18
type S19 = Signed 19
type S20 = Signed 20
type S21 = Signed 21
type S22 = Signed 22
type S23 = Signed 23
type S24 = Signed 24
type S25 = Signed 25
type S26 = Signed 26
type S27 = Signed 27
type S28 = Signed 28
type S29 = Signed 29
type S30 = Signed 30
type S31 = Signed 31
type S32 = Signed 32