{-# LANGUAGE ScopedTypeVariables #-} -- | 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 , toMatrix , fromMatrix , 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.Sized.Matrix as M import Data.Sized.Ix import Data.List as L import Data.Bits newtype Signed ix = Signed Integer -- 'toMatrix' turns a sized 'Signed' value into a 'Matrix' of 'Bool's. toMatrix :: forall ix . (Size ix) => Signed ix -> Matrix ix Bool toMatrix s@(Signed v) = matrix $ take (size (error "toMatrix" :: ix)) $ map odd $ iterate (`div` 2) v -- 'toMatrix' turns a a 'Matrix' of 'Bool's into sized 'Signed' value. fromMatrix :: (Size ix) => Matrix ix Bool -> Signed ix fromMatrix m = mkSigned $ sum [ n | (n,b) <- zip (iterate (* 2) 1) (M.toList m) , b ] -- mkSigned :: forall ix . (Size ix) => Integer -> Signed ix mkSigned v = res where sz' = 2 ^ (fromIntegral bitCount :: Integer) bitCount = size (error "mkUnsigned" :: ix) - 1 res = case divMod v sz' of (s,v') | even s -> Signed v' | otherwise -> Signed (v' - sz') instance (Size ix) => Eq (Signed ix) where (Signed a) == (Signed b) = a == b instance (Size ix) => Ord (Signed ix) where (Signed a) `compare` (Signed b) = a `compare` b instance (Size ix) => Show (Signed ix) where show (Signed a) = show a instance (Enum ix, Size ix) => Read (Signed ix) where readsPrec i str = [ (mkSigned a,r) | (a,r) <- readsPrec i str ] instance (Size 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 (Size 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 (Size ix) => Real (Signed ix) where toRational (Signed n) = toRational n instance (Size ix) => Enum (Signed ix) where fromEnum (Signed n) = fromEnum n toEnum n = mkSigned (toInteger n) instance (Size ix, Integral ix) => Bits (Signed ix) where bitSize s = f s undefined where f :: (Size a) => Signed a -> a -> Int f _ ix = size ix complement = fromMatrix . fmap not . toMatrix isSigned _ = True 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 (Signed v) i = mkSigned (v * (2 ^ i)) shiftR (Signed v) i = mkSigned (v `div` (2 ^ i)) 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 (Signed ix) where minBound = Signed (- maxMagnitude) where maxMagnitude = 2 ^ (size (error "Bounded/Signed" :: ix) -1) maxBound = Signed (maxMagnitude - 1) where maxMagnitude = 2 ^ (size (error "Bounded/Signed" :: ix) -1) type S2 = Signed X2 type S3 = Signed X3 type S4 = Signed X4 type S5 = Signed X5 type S6 = Signed X6 type S7 = Signed X7 type S8 = Signed X8 type S9 = Signed X9 type S10 = Signed X10 type S11 = Signed X11 type S12 = Signed X12 type S13 = Signed X13 type S14 = Signed X14 type S15 = Signed X15 type S16 = Signed X16 type S17 = Signed X17 type S18 = Signed X18 type S19 = Signed X19 type S20 = Signed X20 type S21 = Signed X21 type S22 = Signed X22 type S23 = Signed X23 type S24 = Signed X24 type S25 = Signed X25 type S26 = Signed X26 type S27 = Signed X27 type S28 = Signed X28 type S29 = Signed X29 type S30 = Signed X30 type S31 = Signed X31 type S32 = Signed X32