```{-# LANGUAGE ScopedTypeVariables #-}

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

module Data.Sized.Unsigned
( Unsigned
, toMatrix
, fromMatrix
,      U1,  U2,  U3,  U4,  U5,  U6,  U7,  U8,  U9
, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19
, U20, U21, U22, U23, U24, U25, U26, U27, U28, U29
, U30, U31, U32
) where

import Data.Sized.Matrix as M
import Data.Sized.Ix
import Data.List as L
import Data.Bits

newtype Unsigned ix = Unsigned Integer

toMatrix :: forall ix . (Size ix) => Unsigned ix -> Matrix ix Bool
toMatrix s@(Unsigned v) = matrix \$ take (size (error "toMatrix" :: ix)) \$ map odd \$ iterate (`div` 2) v

fromMatrix :: (Size ix) => Matrix ix Bool -> Unsigned ix
fromMatrix m = mkUnsigned \$
sum [ n
| (n,b) <- zip (iterate (* 2) 1)
(M.toList m)
, b
]

mkUnsigned :: forall ix . (Size ix) => Integer -> Unsigned ix
mkUnsigned v = res
where sz' = 2 ^ (fromIntegral bitCount :: Integer)
bitCount = size (error "mkUnsigned" :: ix)
res = Unsigned (v `mod` sz')

instance (Size ix) => Eq (Unsigned ix) where
(Unsigned a) == (Unsigned b) = a == b
instance (Size ix) => Ord (Unsigned ix) where
(Unsigned a) `compare` (Unsigned b) = a `compare` b
instance (Size ix) => Show (Unsigned ix) where
show (Unsigned a) = show a
instance (Size ix) => Read (Unsigned ix) where
readsPrec i str = [ (mkUnsigned a,r) | (a,r) <- readsPrec i str ]
instance (Size ix) => Integral (Unsigned ix) where
toInteger (Unsigned m) = m
quotRem (Unsigned a) (Unsigned b) =
case quotRem a b of
(q,r) -> (mkUnsigned q,mkUnsigned r)
instance (Size ix) => Num (Unsigned ix) where
(Unsigned a) + (Unsigned b) = mkUnsigned \$ a + b
(Unsigned a) - (Unsigned b) = mkUnsigned \$ a - b
(Unsigned a) * (Unsigned b) = mkUnsigned \$ a * b
abs (Unsigned n) = mkUnsigned \$ abs n
signum (Unsigned n) = mkUnsigned \$ signum n
fromInteger n = mkUnsigned n
instance (Size ix) => Real (Unsigned ix) where
toRational (Unsigned n) = toRational n
instance (Size ix) => Enum (Unsigned ix) where
toEnum n = mkUnsigned (toInteger n)
instance (Size ix, Integral ix) => Bits (Unsigned ix) where
bitSize s = f s undefined
where
f :: (Size a) => Unsigned a -> a -> Int
f _ ix = size ix
complement = fromMatrix . fmap not . toMatrix
isSigned _ = False
a `xor` b = fromMatrix (M.zipWith (/=) (toMatrix a) (toMatrix b))
a .|. b = fromMatrix (M.zipWith (||) (toMatrix a) (toMatrix b))
a .&. b = fromMatrix (M.zipWith (&&) (toMatrix a) (toMatrix b))
shiftL (Unsigned v) i = mkUnsigned (v * (2 ^ i))
shiftR (Unsigned v) i = mkUnsigned (v `div` (2 ^ i))
-- it might be possible to loosen the Integral requirement
rotate v i = fromMatrix (forAll \$ \ ix -> m ! (fromIntegral ((fromIntegral ix - i) `mod` M.length m)))
where m = toMatrix v
testBit u idx = toMatrix u ! (fromIntegral idx)

instance forall ix . (Size ix) => Bounded (Unsigned ix) where
minBound = Unsigned 0
maxBound = Unsigned (2 ^ (size (error "Bounded/Unsigned" :: ix)) - 1)

-- | common; numerically boolean.
type U1 = Unsigned X1

type U2 = Unsigned X2
type U3 = Unsigned X3
type U4 = Unsigned X4
type U5 = Unsigned X5
type U6 = Unsigned X6
type U7 = Unsigned X7
type U8 = Unsigned X8
type U9 = Unsigned X9
type U10 = Unsigned X10
type U11 = Unsigned X11
type U12 = Unsigned X12
type U13 = Unsigned X13
type U14 = Unsigned X14
type U15 = Unsigned X15
type U16 = Unsigned X16
type U17 = Unsigned X17
type U18 = Unsigned X18
type U19 = Unsigned X19
type U20 = Unsigned X20
type U21 = Unsigned X21
type U22 = Unsigned X22
type U23 = Unsigned X23
type U24 = Unsigned X24
type U25 = Unsigned X25
type U26 = Unsigned X26
type U27 = Unsigned X27
type U28 = Unsigned X28
type U29 = Unsigned X29
type U30 = Unsigned X30
type U31 = Unsigned X31
type U32 = Unsigned X32
```