    {-# OPTIONS_GHC -fno-implicit-prelude #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Bits
    -- Copyright   :  (c) The University of Glasgow 2001
    -- License     :  BSD-style (see the file libraries/base/LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- This module defines bitwise operations for signed and unsigned
    -- integers.  Instances of the class 'Bits' for the 'Int' and
    -- 'Integer' types are available from this module, and instances for
    -- explicitly sized integral types are available from the
    -- "Data.Int" and "Data.Word" modules.
    --
    -----------------------------------------------------------------------------

    module Data.Bits (
      Bits(
        (.&.), (.|.), xor, -- :: a -> a -> a
        complement,        -- :: a -> a
        shift,             -- :: a -> Int -> a
        rotate,            -- :: a -> Int -> a
        bit,               -- :: Int -> a
        setBit,            -- :: a -> Int -> a
        clearBit,          -- :: a -> Int -> a
        complementBit,     -- :: a -> Int -> a
        testBit,           -- :: a -> Int -> Bool
        bitSize,           -- :: a -> Int
        isSigned,          -- :: a -> Bool
        shiftL, shiftR,    -- :: a -> Int -> a
        rotateL, rotateR   -- :: a -> Int -> a
      )

      -- instance Bits Int
      -- instance Bits Integer
     ) where

    -- Defines the @Bits@ class containing bit-based operations.
    -- See library document for details on the semantics of the
    -- individual operations.

    #if defined(__GLASGOW_HASKELL__) || defined(__HUGS__)
    #include "MachDeps.h"
    #endif

    #ifdef __GLASGOW_HASKELL__
    import GHC.Num
    import GHC.Real
    import GHC.Base
    #endif

    #ifdef __HUGS__
    import Hugs.Bits
    #endif

    infixl 8 `shift`, `rotate`, `shiftL`, `shiftR`, `rotateL`, `rotateR`
    infixl 7 .&.
    infixl 6 `xor`
    infixl 5 .|.

    {-|
    The 'Bits' class defines bitwise operations over integral types.

    * Bits are numbered from 0 with bit 0 being the least
      significant bit.

    Minimal complete definition: '.&.', '.|.', 'xor', 'complement',
    ('shift' or ('shiftL' and 'shiftR')), ('rotate' or ('rotateL' and 'rotateR')),
    'bitSize' and 'isSigned'.
    -}
    class Num a => Bits a where
        -- | Bitwise \"and\"
        (.&.) :: a -> a -> a

        -- | Bitwise \"or\"
        (.|.) :: a -> a -> a

        -- | Bitwise \"xor\"
        xor :: a -> a -> a

        {-| Reverse all the bits in the argument -}
        complement        :: a -> a

        {-| @'shift' x i@ shifts @x@ left by @i@ bits if @i@ is positive,
            or right by @-i@ bits otherwise.
            Right shifts perform sign extension on signed number types;
            i.e. they fill the top bits with 1 if the @x@ is negative
            and with 0 otherwise.

            An instance can define either this unified 'shift' or 'shiftL' and
            'shiftR', depending on which is more convenient for the type in
            question. -}
        shift             :: a -> Int -> a

        x `shift`   i | i<0  = x `shiftR` (-i)
                      | i==0 = x
                      | i>0  = x `shiftL` i

        {-| @'rotate' x i@ rotates @x@ left by @i@ bits if @i@ is positive,
            or right by @-i@ bits otherwise.

            For unbounded types like 'Integer', 'rotate' is equivalent to 'shift'.

            An instance can define either this unified 'rotate' or 'rotateL' and
            'rotateR', depending on which is more convenient for the type in
            question. -}
        rotate            :: a -> Int -> a

        x `rotate`  i | i<0  = x `rotateR` (-i)
                      | i==0 = x
                      | i>0  = x `rotateL` i

        {-
        -- Rotation can be implemented in terms of two shifts, but care is
        -- needed for negative values.  This suggested implementation assumes
        -- 2's-complement arithmetic.  It is commented out because it would
        -- require an extra context (Ord a) on the signature of 'rotate'.
        x `rotate`  i | i<0 && isSigned x && x<0
                             = let left = i+bitSize x in
                               ((x `shift` i) .&. complement ((-1) `shift` left))
                               .|. (x `shift` left)
                      | i<0  = (x `shift` i) .|. (x `shift` (i+bitSize x))
                      | i==0 = x
                      | i>0  = (x `shift` i) .|. (x `shift` (i-bitSize x))
        -}

        -- | @bit i@ is a value with the @i@th bit set
        bit               :: Int -> a

        -- | @x \`setBit\` i@ is the same as @x .|. bit i@
        setBit            :: a -> Int -> a

        -- | @x \`clearBit\` i@ is the same as @x .&. complement (bit i)@
        clearBit          :: a -> Int -> a

        -- | @x \`complementBit\` i@ is the same as @x \`xor\` bit i@
        complementBit     :: a -> Int -> a

        -- | Return 'True' if the @n@th bit of the argument is 1
        testBit           :: a -> Int -> Bool

        {-| Return the number of bits in the type of the argument.  The actual
            value of the argument is ignored.  The function 'bitSize' is
            undefined for types that do not have a fixed bitsize, like 'Integer'.
            -}
        bitSize           :: a -> Int

        {-| Return 'True' if the argument is a signed type.  The actual
            value of the argument is ignored -}
        isSigned          :: a -> Bool

        bit i               = 1 `shiftL` i
        x `setBit` i        = x .|. bit i
        x `clearBit` i      = x .&. complement (bit i)
        x `complementBit` i = x `xor` bit i
        x `testBit` i       = (x .&. bit i) /= 0

        {-| Shift the argument left by the specified number of bits
            (which must be non-negative).

            An instance can define either this and 'shiftR' or the unified
            'shift', depending on which is more convenient for the type in
            question. -}
        shiftL            :: a -> Int -> a
        x `shiftL`  i = x `shift`  i

        {-| Shift the first argument right by the specified number of bits
            (which must be non-negative).
            Right shifts perform sign extension on signed number types;
            i.e. they fill the top bits with 1 if the @x@ is negative
            and with 0 otherwise.

            An instance can define either this and 'shiftL' or the unified
            'shift', depending on which is more convenient for the type in
            question. -}
        shiftR            :: a -> Int -> a
        x `shiftR`  i = x `shift`  (-i)

        {-| Rotate the argument left by the specified number of bits
            (which must be non-negative).

            An instance can define either this and 'rotateR' or the unified
            'rotate', depending on which is more convenient for the type in
            question. -}
        rotateL           :: a -> Int -> a
        x `rotateL` i = x `rotate` i

        {-| Rotate the argument right by the specified number of bits
            (which must be non-negative).

            An instance can define either this and 'rotateL' or the unified
            'rotate', depending on which is more convenient for the type in
            question. -}
        rotateR           :: a -> Int -> a
        x `rotateR` i = x `rotate` (-i)

    instance Bits Int where
        {-# INLINE shift #-}

    #ifdef __GLASGOW_HASKELL__
        (I# x#) .&.   (I# y#)  = I# (word2Int# (int2Word# x# `and#` int2Word# y#))

        (I# x#) .|.   (I# y#)  = I# (word2Int# (int2Word# x# `or#`  int2Word# y#))

        (I# x#) `xor` (I# y#)  = I# (word2Int# (int2Word# x# `xor#` int2Word# y#))

        complement (I# x#)     = I# (word2Int# (int2Word# x# `xor#` int2Word# (-1#)))

        (I# x#) `shift` (I# i#)
            | i# >=# 0#        = I# (x# `iShiftL#` i#)
            | otherwise        = I# (x# `iShiftRA#` negateInt# i#)

        {-# INLINE rotate #-} 	-- See Note [Constant folding for rotate]
        (I# x#) `rotate` (I# i#) =
            I# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
                           (x'# `uncheckedShiftRL#` (wsib -# i'#))))
          where
            x'# = int2Word# x#
            i'# = word2Int# (int2Word# i# `and#` int2Word# (wsib -# 1#))
            wsib = WORD_SIZE_IN_BITS#   {- work around preprocessor problem (??) -}
        bitSize  _             = WORD_SIZE_IN_BITS
    #else /* !__GLASGOW_HASKELL__ */

    #ifdef __HUGS__
        (.&.)                  = primAndInt
        (.|.)                  = primOrInt
        xor                    = primXorInt
        complement             = primComplementInt
        shift                  = primShiftInt
        bit                    = primBitInt
        testBit                = primTestInt
        bitSize _              = SIZEOF_HSINT*8
    #elif defined(__NHC__)
        (.&.)                  = nhc_primIntAnd
        (.|.)                  = nhc_primIntOr
        xor                    = nhc_primIntXor
        complement             = nhc_primIntCompl
        shiftL                 = nhc_primIntLsh
        shiftR                 = nhc_primIntRsh
        bitSize _              = 32
    #endif /* __NHC__ */

        x `rotate`  i
            | i<0 && x<0       = let left = i+bitSize x in
                                 ((x `shift` i) .&. complement ((-1) `shift` left))
                                 .|. (x `shift` left)
            | i<0              = (x `shift` i) .|. (x `shift` (i+bitSize x))
            | i==0             = x
            | i>0              = (x `shift` i) .|. (x `shift` (i-bitSize x))

    #endif /* !__GLASGOW_HASKELL__ */

        isSigned _             = True

    #ifdef __NHC__
    foreign import ccall nhc_primIntAnd :: Int -> Int -> Int
    foreign import ccall nhc_primIntOr  :: Int -> Int -> Int
    foreign import ccall nhc_primIntXor :: Int -> Int -> Int
    foreign import ccall nhc_primIntLsh :: Int -> Int -> Int
    foreign import ccall nhc_primIntRsh :: Int -> Int -> Int
    foreign import ccall nhc_primIntCompl :: Int -> Int
    #endif /* __NHC__ */

    instance Bits Integer where
    #ifdef __GLASGOW_HASKELL__
       (S# x) .&. (S# y) = S# (word2Int# (int2Word# x `and#` int2Word# y))
       x@(S# _) .&. y = toBig x .&. y
       x .&. y@(S# _) = x .&. toBig y
       (J# s1 d1) .&. (J# s2 d2) =
            case andInteger# s1 d1 s2 d2 of
              (# s, d #) -> J# s d

       (S# x) .|. (S# y) = S# (word2Int# (int2Word# x `or#` int2Word# y))
       x@(S# _) .|. y = toBig x .|. y
       x .|. y@(S# _) = x .|. toBig y
       (J# s1 d1) .|. (J# s2 d2) =
            case orInteger# s1 d1 s2 d2 of
              (# s, d #) -> J# s d

       (S# x) `xor` (S# y) = S# (word2Int# (int2Word# x `xor#` int2Word# y))
       x@(S# _) `xor` y = toBig x `xor` y
       x `xor` y@(S# _) = x `xor` toBig y
       (J# s1 d1) `xor` (J# s2 d2) =
            case xorInteger# s1 d1 s2 d2 of
              (# s, d #) -> J# s d

       complement (S# x) = S# (word2Int# (int2Word# x `xor#` int2Word# (0# -# 1#)))
       complement (J# s d) = case complementInteger# s d of (# s, d #) -> J# s d
    #else
       -- reduce bitwise binary operations to special cases we can handle

       x .&. y   | x<0 && y<0 = complement (complement x `posOr` complement y)
                 | otherwise  = x `posAnd` y

       x .|. y   | x<0 || y<0 = complement (complement x `posAnd` complement y)
                 | otherwise  = x `posOr` y

       x `xor` y | x<0 && y<0 = complement x `posXOr` complement y
                 | x<0        = complement (complement x `posXOr` y)
                 |        y<0 = complement (x `posXOr` complement y)
                 | otherwise  = x `posXOr` y

       -- assuming infinite 2's-complement arithmetic
       complement a = -1 - a
    #endif

       shift x i | i >= 0    = x * 2^i
                 | otherwise = x `div` 2^(-i)

       rotate x i = shift x i   -- since an Integer never wraps around

       bitSize _  = error "Data.Bits.bitSize(Integer)"
       isSigned _ = True

    #ifndef __GLASGOW_HASKELL__
    -- Crude implementation of bitwise operations on Integers: convert them
    -- to finite lists of Ints (least significant first), zip and convert
    -- back again.

    -- posAnd requires at least one argument non-negative
    -- posOr and posXOr require both arguments non-negative

    posAnd, posOr, posXOr :: Integer -> Integer -> Integer
    posAnd x y   = fromInts $ zipWith (.&.) (toInts x) (toInts y)
    posOr x y    = fromInts $ longZipWith (.|.) (toInts x) (toInts y)
    posXOr x y   = fromInts $ longZipWith xor (toInts x) (toInts y)

    longZipWith :: (a -> a -> a) -> [a] -> [a] -> [a]
    longZipWith f xs [] = xs
    longZipWith f [] ys = ys
    longZipWith f (x:xs) (y:ys) = f x y:longZipWith f xs ys

    toInts :: Integer -> [Int]
    toInts n
        | n == 0 = []
        | otherwise = mkInt (n `mod` numInts):toInts (n `div` numInts)
      where mkInt n | n > toInteger(maxBound::Int) = fromInteger (n-numInts)
                    | otherwise = fromInteger n

    fromInts :: [Int] -> Integer
    fromInts = foldr catInt 0
        where catInt d n = (if d<0 then n+1 else n)*numInts + toInteger d

    numInts = toInteger (maxBound::Int) - toInteger (minBound::Int) + 1
    #endif /* !__GLASGOW_HASKELL__ */

    {- 	Note [Constant folding for rotate]
    	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    The INLINE on the Int instance of rotate enables it to be constant
    folded.  For example:
         sumU . mapU (`rotate` 3) . replicateU 10000000 $ (7 :: Int)
    goes to:
       Main.$wfold =
         \ (ww_sO7 :: Int#) (ww1_sOb :: Int#) ->
           case ww1_sOb of wild_XM {
             __DEFAULT -> Main.$wfold (+# ww_sO7 56) (+# wild_XM 1);
             10000000 -> ww_sO7
    whereas before it was left as a call to $wrotate.

    All other Bits instances seem to inline well enough on their
    own to enable constant folding; for example 'shift':
         sumU . mapU (`shift` 3) . replicateU 10000000 $ (7 :: Int)
     goes to:
         Main.$wfold =
           \ (ww_sOb :: Int#) (ww1_sOf :: Int#) ->
             case ww1_sOf of wild_XM {
               __DEFAULT -> Main.$wfold (+# ww_sOb 56) (+# wild_XM 1);
               10000000 -> ww_sOb
             }
    -}