    {-# LANGUAGE BangPatterns #-}
    {-# LANGUAGE CPP #-}
    {-# LANGUAGE NoImplicitPrelude #-}
    {-# LANGUAGE MagicHash #-}
    {-# LANGUAGE Trustworthy #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.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 GHC.Bits (
      Bits(
        (.&.), (.|.), xor,
        complement,
        shift,
        rotate,
        zeroBits,
        bit,
        setBit,
        clearBit,
        complementBit,
        testBit,
        bitSizeMaybe,
        bitSize,
        isSigned,
        shiftL, shiftR,
        unsafeShiftL, unsafeShiftR,
        rotateL, rotateR,
        popCount
      ),
      FiniteBits(
        finiteBitSize,
        countLeadingZeros,
        countTrailingZeros
      ),

      bitDefault,
      testBitDefault,
      popCountDefault,
      toIntegralSized,
     ) where

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

    #include "MachDeps.h"

    import Data.Maybe
    import GHC.Num
    import GHC.Base
    import GHC.Real

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

    {-# DEPRECATED bitSize "Use 'bitSizeMaybe' or 'finiteBitSize' instead" #-} -- deprecated in 7.8

    -- | The 'Bits' class defines bitwise operations over integral types.
    --
    -- * Bits are numbered from 0 with bit 0 being the least
    --   significant bit.
    class Eq a => Bits a where
        {-# MINIMAL (.&.), (.|.), xor, complement,
                    (shift | (shiftL, shiftR)),
                    (rotate | (rotateL, rotateR)),
                    bitSize, bitSizeMaybe, isSigned, testBit, bit, popCount #-}

        -- | 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

        a
    x `shift`   Int
    i | Int
    iforall a. Ord a => a -> a -> Bool
    <Int
    0       = a
    x forall a. Bits a => a -> Int -> a
    `shiftR` (-Int
    i)
                      | Int
    iforall a. Ord a => a -> a -> Bool
    >Int
    0       = a
    x forall a. Bits a => a -> Int -> a
    `shiftL` Int
    i
                      | Bool
    otherwise = a
    x

        {-| @'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

        a
    x `rotate`  Int
    i | Int
    iforall a. Ord a => a -> a -> Bool
    <Int
    0       = a
    x forall a. Bits a => a -> Int -> a
    `rotateR` (-Int
    i)
                      | Int
    iforall a. Ord a => a -> a -> Bool
    >Int
    0       = a
    x forall a. Bits a => a -> Int -> a
    `rotateL` Int
    i
                      | Bool
    otherwise = a
    x

        {-
        -- 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))
        -}

        -- | 'zeroBits' is the value with all bits unset.
        --
        -- The following laws ought to hold (for all valid bit indices @/n/@):
        --
        --   * @'clearBit' 'zeroBits' /n/ == 'zeroBits'@
        --   * @'setBit'   'zeroBits' /n/ == 'bit' /n/@
        --   * @'testBit'  'zeroBits' /n/ == False@
        --   * @'popCount' 'zeroBits'   == 0@
        --
        -- This method uses @'clearBit' ('bit' 0) 0@ as its default
        -- implementation (which ought to be equivalent to 'zeroBits' for
        -- types which possess a 0th bit).
        --
        -- @since 4.7.0.0
        zeroBits :: a
        zeroBits = forall a. Bits a => a -> Int -> a
    clearBit (forall a. Bits a => Int -> a
    bit Int
    0) Int
    0

        -- | @bit /i/@ is a value with the @/i/@th bit set and all other bits clear.
        --
        -- Can be implemented using `bitDefault' if @a@ is also an
        -- instance of 'Num'.
        --
        -- See also 'zeroBits'.
        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

        {-| @x \`testBit\` i@ is the same as @x .&. bit n /= 0@

            In other words it returns True if the bit at offset @n
            is set.

            Can be implemented using `testBitDefault' if @a@ is also an
            instance of 'Num'.
            -}
        testBit           :: a -> Int -> Bool

        {-| Return the number of bits in the type of the argument.  The actual
            value of the argument is ignored.  Returns Nothing
            for types that do not have a fixed bitsize, like 'Integer'.

            @since 4.7.0.0
            -}
        bitSizeMaybe      :: a -> Maybe Int

        {-| 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'.

            Default implementation based upon 'bitSizeMaybe' provided since
            4.12.0.0.
            -}
        bitSize           :: a -> Int
        bitSize a
    b = forall a. a -> Maybe a -> a
    fromMaybe (forall a. HasCallStack => [Char] -> a
    error [Char]
    "bitSize is undefined") (forall a. Bits a => a -> Maybe Int
    bitSizeMaybe a
    b)

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

        {-# INLINE setBit #-}
        {-# INLINE clearBit #-}
        {-# INLINE complementBit #-}
        a
    x `setBit` Int
    i        = a
    x forall a. Bits a => a -> a -> a
    .|. forall a. Bits a => Int -> a
    bit Int
    i
        a
    x `clearBit` Int
    i      = a
    x forall a. Bits a => a -> a -> a
    .&. forall a. Bits a => a -> a
    complement (forall a. Bits a => Int -> a
    bit Int
    i)
        a
    x `complementBit` Int
    i = a
    x forall a. Bits a => a -> a -> a
    `xor` forall a. Bits a => Int -> a
    bit Int
    i

        {-| Shift the argument left by the specified number of bits
            (which must be non-negative). Some instances may throw an
            'Control.Exception.Overflow' exception if given a negative input.

            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
        {-# INLINE shiftL #-}
        a
    x `shiftL`  Int
    i = a
    x forall a. Bits a => a -> Int -> a
    `shift`  Int
    i

        {-| Shift the argument left by the specified number of bits.  The
            result is undefined for negative shift amounts and shift amounts
            greater or equal to the 'bitSize'.

            Defaults to 'shiftL' unless defined explicitly by an instance.

            @since 4.5.0.0 -}
        unsafeShiftL            :: a -> Int -> a
        {-# INLINE unsafeShiftL #-}
        a
    x `unsafeShiftL` Int
    i = a
    x forall a. Bits a => a -> Int -> a
    `shiftL` Int
    i

        {-| Shift the first argument right by the specified number of bits. The
            result is undefined for negative shift amounts and shift amounts
            greater or equal to the 'bitSize'. Some instances may throw an
            'Control.Exception.Overflow' exception if given a negative input.

            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
        {-# INLINE shiftR #-}
        a
    x `shiftR`  Int
    i = a
    x forall a. Bits a => a -> Int -> a
    `shift`  (-Int
    i)

        {-| Shift the first argument right by the specified number of bits, which
            must be non-negative and smaller than the number of bits in the type.

            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.

            Defaults to 'shiftR' unless defined explicitly by an instance.

            @since 4.5.0.0 -}
        unsafeShiftR            :: a -> Int -> a
        {-# INLINE unsafeShiftR #-}
        a
    x `unsafeShiftR` Int
    i = a
    x forall a. Bits a => a -> Int -> a
    `shiftR` Int
    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
        {-# INLINE rotateL #-}
        a
    x `rotateL` Int
    i = a
    x forall a. Bits a => a -> Int -> a
    `rotate` Int
    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
        {-# INLINE rotateR #-}
        a
    x `rotateR` Int
    i = a
    x forall a. Bits a => a -> Int -> a
    `rotate` (-Int
    i)

        {-| Return the number of set bits in the argument.  This number is
            known as the population count or the Hamming weight.

            Can be implemented using `popCountDefault' if @a@ is also an
            instance of 'Num'.

            @since 4.5.0.0 -}
        popCount          :: a -> Int

    -- |The 'FiniteBits' class denotes types with a finite, fixed number of bits.
    --
    -- @since 4.7.0.0
    class Bits b => FiniteBits b where
        -- | Return the number of bits in the type of the argument.
        -- The actual value of the argument is ignored. Moreover, 'finiteBitSize'
        -- is total, in contrast to the deprecated 'bitSize' function it replaces.
        --
        -- @
        -- 'finiteBitSize' = 'bitSize'
        -- 'bitSizeMaybe' = 'Just' . 'finiteBitSize'
        -- @
        --
        -- @since 4.7.0.0
        finiteBitSize :: b -> Int

        -- | Count number of zero bits preceding the most significant set bit.
        --
        -- @
        -- 'countLeadingZeros' ('zeroBits' :: a) = finiteBitSize ('zeroBits' :: a)
        -- @
        --
        -- 'countLeadingZeros' can be used to compute log base 2 via
        --
        -- @
        -- logBase2 x = 'finiteBitSize' x - 1 - 'countLeadingZeros' x
        -- @
        --
        -- Note: The default implementation for this method is intentionally
        -- naive. However, the instances provided for the primitive
        -- integral types are implemented using CPU specific machine
        -- instructions.
        --
        -- @since 4.8.0.0
        countLeadingZeros :: b -> Int
        countLeadingZeros b
    x = (Int
    wforall a. Num a => a -> a -> a
    -Int
    1) forall a. Num a => a -> a -> a
    - Int -> Int
    go (Int
    wforall a. Num a => a -> a -> a
    -Int
    1)
          where
            go :: Int -> Int
    go Int
    i | Int
    i forall a. Ord a => a -> a -> Bool
    < Int
    0       = Int
    i -- no bit set
                 | forall a. Bits a => a -> Int -> Bool
    testBit b
    x Int
    i = Int
    i
                 | Bool
    otherwise   = Int -> Int
    go (Int
    iforall a. Num a => a -> a -> a
    -Int
    1)

            w :: Int
    w = forall b. FiniteBits b => b -> Int
    finiteBitSize b
    x

        -- | Count number of zero bits following the least significant set bit.
        --
        -- @
        -- 'countTrailingZeros' ('zeroBits' :: a) = finiteBitSize ('zeroBits' :: a)
        -- 'countTrailingZeros' . 'negate' = 'countTrailingZeros'
        -- @
        --
        -- The related
        -- <http://en.wikipedia.org/wiki/Find_first_set find-first-set operation>
        -- can be expressed in terms of 'countTrailingZeros' as follows
        --
        -- @
        -- findFirstSet x = 1 + 'countTrailingZeros' x
        -- @
        --
        -- Note: The default implementation for this method is intentionally
        -- naive. However, the instances provided for the primitive
        -- integral types are implemented using CPU specific machine
        -- instructions.
        --
        -- @since 4.8.0.0
        countTrailingZeros :: b -> Int
        countTrailingZeros b
    x = Int -> Int
    go Int
    0
          where
            go :: Int -> Int
    go Int
    i | Int
    i forall a. Ord a => a -> a -> Bool
    >= Int
    w      = Int
    i
                 | forall a. Bits a => a -> Int -> Bool
    testBit b
    x Int
    i = Int
    i
                 | Bool
    otherwise   = Int -> Int
    go (Int
    iforall a. Num a => a -> a -> a
    +Int
    1)

            w :: Int
    w = forall b. FiniteBits b => b -> Int
    finiteBitSize b
    x

    -- The defaults below are written with lambdas so that e.g.
    --     bit = bitDefault
    -- is fully applied, so inlining will happen

    -- | Default implementation for 'bit'.
    --
    -- Note that: @bitDefault i = 1 `shiftL` i@
    --
    -- @since 4.6.0.0
    bitDefault :: (Bits a, Num a) => Int -> a
    bitDefault :: forall a. (Bits a, Num a) => Int -> a
    bitDefault = \Int
    i -> a
    1 forall a. Bits a => a -> Int -> a
    `shiftL` Int
    i
    {-# INLINE bitDefault #-}

    -- | Default implementation for 'testBit'.
    --
    -- Note that: @testBitDefault x i = (x .&. bit i) /= 0@
    --
    -- @since 4.6.0.0
    testBitDefault ::  (Bits a, Num a) => a -> Int -> Bool
    testBitDefault :: forall a. (Bits a, Num a) => a -> Int -> Bool
    testBitDefault = \a
    x Int
    i -> (a
    x forall a. Bits a => a -> a -> a
    .&. forall a. Bits a => Int -> a
    bit Int
    i) forall a. Eq a => a -> a -> Bool
    /= a
    0
    {-# INLINE testBitDefault #-}

    -- | Default implementation for 'popCount'.
    --
    -- This implementation is intentionally naive. Instances are expected to provide
    -- an optimized implementation for their size.
    --
    -- @since 4.6.0.0
    popCountDefault :: (Bits a, Num a) => a -> Int
    popCountDefault :: forall a. (Bits a, Num a) => a -> Int
    popCountDefault = forall {t} {t}. (Num t, Num t, Bits t) => t -> t -> t
    go Int
    0
     where
       go :: t -> t -> t
    go !t
    c t
    0 = t
    c
       go t
    c t
    w = t -> t -> t
    go (t
    cforall a. Num a => a -> a -> a
    +t
    1) (t
    w forall a. Bits a => a -> a -> a
    .&. (t
    w forall a. Num a => a -> a -> a
    - t
    1)) -- clear the least significant
    {-# INLINABLE popCountDefault #-}

    -- | Interpret 'Bool' as 1-bit bit-field
    --
    --  @since 4.7.0.0
    instance Bits Bool where
        .&. :: Bool -> Bool -> Bool
    (.&.) = Bool -> Bool -> Bool
    (&&)

        .|. :: Bool -> Bool -> Bool
    (.|.) = Bool -> Bool -> Bool
    (||)

        xor :: Bool -> Bool -> Bool
    xor = forall a. Eq a => a -> a -> Bool
    (/=)

        complement :: Bool -> Bool
    complement = Bool -> Bool
    not

        shift :: Bool -> Int -> Bool
    shift Bool
    x Int
    0 = Bool
    x
        shift Bool
    _ Int
    _ = Bool
    False

        rotate :: Bool -> Int -> Bool
    rotate Bool
    x Int
    _ = Bool
    x

        bit :: Int -> Bool
    bit Int
    0 = Bool
    True
        bit Int
    _ = Bool
    False

        testBit :: Bool -> Int -> Bool
    testBit Bool
    x Int
    0 = Bool
    x
        testBit Bool
    _ Int
    _ = Bool
    False

        bitSizeMaybe :: Bool -> Maybe Int
    bitSizeMaybe Bool
    _ = forall a. a -> Maybe a
    Just Int
    1

        bitSize :: Bool -> Int
    bitSize Bool
    _ = Int
    1

        isSigned :: Bool -> Bool
    isSigned Bool
    _ = Bool
    False

        popCount :: Bool -> Int
    popCount Bool
    False = Int
    0
        popCount Bool
    True  = Int
    1

    -- | @since 4.7.0.0
    instance FiniteBits Bool where
        finiteBitSize :: Bool -> Int
    finiteBitSize Bool
    _ = Int
    1
        countTrailingZeros :: Bool -> Int
    countTrailingZeros Bool
    x = if Bool
    x then Int
    0 else Int
    1
        countLeadingZeros :: Bool -> Int
    countLeadingZeros  Bool
    x = if Bool
    x then Int
    0 else Int
    1

    -- | @since 2.01
    instance Bits Int where
        {-# INLINE shift #-}
        {-# INLINE bit #-}
        {-# INLINE testBit #-}
        -- We want popCnt# to be inlined in user code so that `ghc -msse4.2`
        -- can compile it down to a popcnt instruction without an extra function call
        {-# INLINE popCount #-}

        zeroBits :: Int
    zeroBits = Int
    0

        bit :: Int -> Int
    bit     = forall a. (Bits a, Num a) => Int -> a
    bitDefault

        testBit :: Int -> Int -> Bool
    testBit = forall a. (Bits a, Num a) => a -> Int -> Bool
    testBitDefault

        (I# Int#
    x#) .&. :: Int -> Int -> Int
    .&.   (I# Int#
    y#)          = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `andI#` Int#
    y#)
        (I# Int#
    x#) .|. :: Int -> Int -> Int
    .|.   (I# Int#
    y#)          = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `orI#`  Int#
    y#)
        (I# Int#
    x#) xor :: Int -> Int -> Int
    `xor` (I# Int#
    y#)          = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `xorI#` Int#
    y#)
        complement :: Int -> Int
    complement (I# Int#
    x#)             = Int# -> Int
    I# (Int# -> Int#
    notI# Int#
    x#)
        (I# Int#
    x#) shift :: Int -> Int -> Int
    `shift` (I# Int#
    i#)
            | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#)      = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `iShiftL#` Int#
    i#)
            | Bool
    otherwise                = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `iShiftRA#` Int# -> Int#
    negateInt# Int#
    i#)
        (I# Int#
    x#) shiftL :: Int -> Int -> Int
    `shiftL` (I# Int#
    i#)
            | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#)      = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `iShiftL#` Int#
    i#)
            | Bool
    otherwise                = forall a. a
    overflowError
        (I# Int#
    x#) unsafeShiftL :: Int -> Int -> Int
    `unsafeShiftL` (I# Int#
    i#) = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `uncheckedIShiftL#` Int#
    i#)
        (I# Int#
    x#) shiftR :: Int -> Int -> Int
    `shiftR` (I# Int#
    i#)
            | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#)      = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `iShiftRA#` Int#
    i#)
            | Bool
    otherwise                = forall a. a
    overflowError
        (I# Int#
    x#) unsafeShiftR :: Int -> Int -> Int
    `unsafeShiftR` (I# Int#
    i#) = Int# -> Int
    I# (Int#
    x# Int# -> Int# -> Int#
    `uncheckedIShiftRA#` Int#
    i#)

        {-# INLINE rotate #-}       -- See Note [Constant folding for rotate]
        (I# Int#
    x#) rotate :: Int -> Int -> Int
    `rotate` (I# Int#
    i#) =
            Int# -> Int
    I# ((Int#
    x# Int# -> Int# -> Int#
    `uncheckedIShiftL#` Int#
    i'#) Int# -> Int# -> Int#
    `orI#` (Int#
    x# Int# -> Int# -> Int#
    `uncheckedIShiftRL#` (Int#
    wsib Int# -> Int# -> Int#
    -# Int#
    i'#)))
          where
            !i'# :: Int#
    i'# = Int#
    i# Int# -> Int# -> Int#
    `andI#` (Int#
    wsib Int# -> Int# -> Int#
    -# Int#
    1#)
            !wsib :: Int#
    wsib = WORD_SIZE_IN_BITS#   {- work around preprocessor problem (??) -}
        bitSizeMaybe :: Int -> Maybe Int
    bitSizeMaybe Int
    i         = forall a. a -> Maybe a
    Just (forall b. FiniteBits b => b -> Int
    finiteBitSize Int
    i)
        bitSize :: Int -> Int
    bitSize Int
    i              = forall b. FiniteBits b => b -> Int
    finiteBitSize Int
    i

        popCount :: Int -> Int
    popCount (I# Int#
    x#) = Int# -> Int
    I# (Word# -> Int#
    word2Int# (Word# -> Word#
    popCnt# (Int# -> Word#
    int2Word# Int#
    x#)))

        isSigned :: Int -> Bool
    isSigned Int
    _             = Bool
    True

    -- | @since 4.6.0.0
    instance FiniteBits Int where
        finiteBitSize :: Int -> Int
    finiteBitSize Int
    _ = WORD_SIZE_IN_BITS
        countLeadingZeros :: Int -> Int
    countLeadingZeros  (I# Int#
    x#) = Int# -> Int
    I# (Word# -> Int#
    word2Int# (Word# -> Word#
    clz# (Int# -> Word#
    int2Word# Int#
    x#)))
        {-# INLINE countLeadingZeros #-}
        countTrailingZeros :: Int -> Int
    countTrailingZeros (I# Int#
    x#) = Int# -> Int
    I# (Word# -> Int#
    word2Int# (Word# -> Word#
    ctz# (Int# -> Word#
    int2Word# Int#
    x#)))
        {-# INLINE countTrailingZeros #-}

    -- | @since 2.01
    instance Bits Word where
        {-# INLINE shift #-}
        {-# INLINE bit #-}
        {-# INLINE testBit #-}
        {-# INLINE popCount #-}

        (W# Word#
    x#) .&. :: Word -> Word -> Word
    .&.   (W# Word#
    y#)    = Word# -> Word
    W# (Word#
    x# Word# -> Word# -> Word#
    `and#` Word#
    y#)
        (W# Word#
    x#) .|. :: Word -> Word -> Word
    .|.   (W# Word#
    y#)    = Word# -> Word
    W# (Word#
    x# Word# -> Word# -> Word#
    `or#`  Word#
    y#)
        (W# Word#
    x#) xor :: Word -> Word -> Word
    `xor` (W# Word#
    y#)    = Word# -> Word
    W# (Word#
    x# Word# -> Word# -> Word#
    `xor#` Word#
    y#)
        complement :: Word -> Word
    complement (W# Word#
    x#)       = Word# -> Word
    W# (Word# -> Word#
    not# Word#
    x#)
        (W# Word#
    x#) shift :: Word -> Int -> Word
    `shift` (I# Int#
    i#)
            | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#)      = Word# -> Word
    W# (Word#
    x# Word# -> Int# -> Word#
    `shiftL#` Int#
    i#)
            | Bool
    otherwise                = Word# -> Word
    W# (Word#
    x# Word# -> Int# -> Word#
    `shiftRL#` Int# -> Int#
    negateInt# Int#
    i#)
        (W# Word#
    x#) shiftL :: Word -> Int -> Word
    `shiftL` (I# Int#
    i#)
            | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#)      = Word# -> Word
    W# (Word#
    x# Word# -> Int# -> Word#
    `shiftL#` Int#
    i#)
            | Bool
    otherwise                = forall a. a
    overflowError
        (W# Word#
    x#) unsafeShiftL :: Word -> Int -> Word
    `unsafeShiftL` (I# Int#
    i#) = Word# -> Word
    W# (Word#
    x# Word# -> Int# -> Word#
    `uncheckedShiftL#` Int#
    i#)
        (W# Word#
    x#) shiftR :: Word -> Int -> Word
    `shiftR` (I# Int#
    i#)
            | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#)      = Word# -> Word
    W# (Word#
    x# Word# -> Int# -> Word#
    `shiftRL#` Int#
    i#)
            | Bool
    otherwise                = forall a. a
    overflowError
        (W# Word#
    x#) unsafeShiftR :: Word -> Int -> Word
    `unsafeShiftR` (I# Int#
    i#) = Word# -> Word
    W# (Word#
    x# Word# -> Int# -> Word#
    `uncheckedShiftRL#` Int#
    i#)
        (W# Word#
    x#) rotate :: Word -> Int -> Word
    `rotate` (I# Int#
    i#)
            | Int# -> Bool
    isTrue# (Int#
    i'# Int# -> Int# -> Int#
    ==# Int#
    0#) = Word# -> Word
    W# Word#
    x#
            | Bool
    otherwise  = Word# -> Word
    W# ((Word#
    x# Word# -> Int# -> Word#
    `uncheckedShiftL#` Int#
    i'#) Word# -> Word# -> Word#
    `or#` (Word#
    x# Word# -> Int# -> Word#
    `uncheckedShiftRL#` (Int#
    wsib Int# -> Int# -> Int#
    -# Int#
    i'#)))
            where
            !i'# :: Int#
    i'# = Int#
    i# Int# -> Int# -> Int#
    `andI#` (Int#
    wsib Int# -> Int# -> Int#
    -# Int#
    1#)
            !wsib :: Int#
    wsib = WORD_SIZE_IN_BITS#  {- work around preprocessor problem (??) -}
        bitSizeMaybe :: Word -> Maybe Int
    bitSizeMaybe Word
    i           = forall a. a -> Maybe a
    Just (forall b. FiniteBits b => b -> Int
    finiteBitSize Word
    i)
        bitSize :: Word -> Int
    bitSize Word
    i                = forall b. FiniteBits b => b -> Int
    finiteBitSize Word
    i
        isSigned :: Word -> Bool
    isSigned Word
    _               = Bool
    False
        popCount :: Word -> Int
    popCount (W# Word#
    x#)         = Int# -> Int
    I# (Word# -> Int#
    word2Int# (Word# -> Word#
    popCnt# Word#
    x#))
        bit :: Int -> Word
    bit                      = forall a. (Bits a, Num a) => Int -> a
    bitDefault
        testBit :: Word -> Int -> Bool
    testBit                  = forall a. (Bits a, Num a) => a -> Int -> Bool
    testBitDefault

    -- | @since 4.6.0.0
    instance FiniteBits Word where
        finiteBitSize :: Word -> Int
    finiteBitSize Word
    _ = WORD_SIZE_IN_BITS
        countLeadingZeros :: Word -> Int
    countLeadingZeros  (W# Word#
    x#) = Int# -> Int
    I# (Word# -> Int#
    word2Int# (Word# -> Word#
    clz# Word#
    x#))
        {-# INLINE countLeadingZeros #-}
        countTrailingZeros :: Word -> Int
    countTrailingZeros (W# Word#
    x#) = Int# -> Int
    I# (Word# -> Int#
    word2Int# (Word# -> Word#
    ctz# Word#
    x#))
        {-# INLINE countTrailingZeros #-}

    -- | @since 2.01
    instance Bits Integer where
       .&. :: Integer -> Integer -> Integer
    (.&.)      = Integer -> Integer -> Integer
    integerAnd
       .|. :: Integer -> Integer -> Integer
    (.|.)      = Integer -> Integer -> Integer
    integerOr
       xor :: Integer -> Integer -> Integer
    xor        = Integer -> Integer -> Integer
    integerXor
       complement :: Integer -> Integer
    complement = Integer -> Integer
    integerComplement
       unsafeShiftR :: Integer -> Int -> Integer
    unsafeShiftR Integer
    x Int
    i = Integer -> Word -> Integer
    integerShiftR Integer
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
       unsafeShiftL :: Integer -> Int -> Integer
    unsafeShiftL Integer
    x Int
    i = Integer -> Word -> Integer
    integerShiftL Integer
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
       shiftR :: Integer -> Int -> Integer
    shiftR Integer
    x i :: Int
    i@(I# Int#
    i#)
          | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#) = forall a. Bits a => a -> Int -> a
    unsafeShiftR Integer
    x Int
    i
          | Bool
    otherwise           = forall a. a
    overflowError
       shiftL :: Integer -> Int -> Integer
    shiftL Integer
    x i :: Int
    i@(I# Int#
    i#)
          | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#) = forall a. Bits a => a -> Int -> a
    unsafeShiftL Integer
    x Int
    i
          | Bool
    otherwise           = forall a. a
    overflowError
       shift :: Integer -> Int -> Integer
    shift Integer
    x Int
    i | Int
    i forall a. Ord a => a -> a -> Bool
    >= Int
    0    = Integer -> Word -> Integer
    integerShiftL Integer
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
                 | Bool
    otherwise = Integer -> Word -> Integer
    integerShiftR Integer
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral (forall a. Num a => a -> a
    negate Int
    i))
       testBit :: Integer -> Int -> Bool
    testBit Integer
    x Int
    i = Integer -> Word -> Bool
    integerTestBit Integer
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
       zeroBits :: Integer
    zeroBits    = Integer
    integerZero

       bit :: Int -> Integer
    bit (I# Int#
    i)  = Word# -> Integer
    integerBit# (Int# -> Word#
    int2Word# Int#
    i)
       popCount :: Integer -> Int
    popCount Integer
    x  = Int# -> Int
    I# (Integer -> Int#
    integerPopCount# Integer
    x)

       rotate :: Integer -> Int -> Integer
    rotate Integer
    x Int
    i = forall a. Bits a => a -> Int -> a
    shift Integer
    x Int
    i   -- since an Integer never wraps around

       bitSizeMaybe :: Integer -> Maybe Int
    bitSizeMaybe Integer
    _ = forall a. Maybe a
    Nothing
       bitSize :: Integer -> Int
    bitSize Integer
    _  = forall a. [Char] -> a
    errorWithoutStackTrace [Char]
    "Data.Bits.bitSize(Integer)"
       isSigned :: Integer -> Bool
    isSigned Integer
    _ = Bool
    True

    -- | @since 4.8.0
    instance Bits Natural where
       .&. :: Natural -> Natural -> Natural
    (.&.)         = Natural -> Natural -> Natural
    naturalAnd
       .|. :: Natural -> Natural -> Natural
    (.|.)         = Natural -> Natural -> Natural
    naturalOr
       xor :: Natural -> Natural -> Natural
    xor           = Natural -> Natural -> Natural
    naturalXor
       complement :: Natural -> Natural
    complement Natural
    _  = forall a. [Char] -> a
    errorWithoutStackTrace
                        [Char]
    "Bits.complement: Natural complement undefined"
       unsafeShiftR :: Natural -> Int -> Natural
    unsafeShiftR Natural
    x Int
    i = Natural -> Word -> Natural
    naturalShiftR Natural
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
       unsafeShiftL :: Natural -> Int -> Natural
    unsafeShiftL Natural
    x Int
    i = Natural -> Word -> Natural
    naturalShiftL Natural
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
       shiftR :: Natural -> Int -> Natural
    shiftR Natural
    x i :: Int
    i@(I# Int#
    i#)
          | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#) = forall a. Bits a => a -> Int -> a
    unsafeShiftR Natural
    x Int
    i
          | Bool
    otherwise           = forall a. a
    overflowError
       shiftL :: Natural -> Int -> Natural
    shiftL Natural
    x i :: Int
    i@(I# Int#
    i#)
          | Int# -> Bool
    isTrue# (Int#
    i# Int# -> Int# -> Int#
    >=# Int#
    0#) = forall a. Bits a => a -> Int -> a
    unsafeShiftL Natural
    x Int
    i
          | Bool
    otherwise           = forall a. a
    overflowError
       shift :: Natural -> Int -> Natural
    shift Natural
    x Int
    i
         | Int
    i forall a. Ord a => a -> a -> Bool
    >= Int
    0    = Natural -> Word -> Natural
    naturalShiftL Natural
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
         | Bool
    otherwise = Natural -> Word -> Natural
    naturalShiftR Natural
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral (forall a. Num a => a -> a
    negate Int
    i))
       testBit :: Natural -> Int -> Bool
    testBit Natural
    x Int
    i   = Natural -> Word -> Bool
    naturalTestBit Natural
    x (forall a b. (Integral a, Num b) => a -> b
    fromIntegral Int
    i)
       zeroBits :: Natural
    zeroBits      = Natural
    naturalZero
       clearBit :: Natural -> Int -> Natural
    clearBit Natural
    x Int
    i  = Natural
    x forall a. Bits a => a -> a -> a
    `xor` (forall a. Bits a => Int -> a
    bit Int
    i forall a. Bits a => a -> a -> a
    .&. Natural
    x)

       bit :: Int -> Natural
    bit (I# Int#
    i)  = Word# -> Natural
    naturalBit# (Int# -> Word#
    int2Word# Int#
    i)
       popCount :: Natural -> Int
    popCount Natural
    x  = Int# -> Int
    I# (Word# -> Int#
    word2Int# (Natural -> Word#
    naturalPopCount# Natural
    x))

       rotate :: Natural -> Int -> Natural
    rotate Natural
    x Int
    i = forall a. Bits a => a -> Int -> a
    shift Natural
    x Int
    i   -- since an Natural never wraps around

       bitSizeMaybe :: Natural -> Maybe Int
    bitSizeMaybe Natural
    _ = forall a. Maybe a
    Nothing
       bitSize :: Natural -> Int
    bitSize Natural
    _  = forall a. [Char] -> a
    errorWithoutStackTrace [Char]
    "Data.Bits.bitSize(Natural)"
       isSigned :: Natural -> Bool
    isSigned Natural
    _ = Bool
    False

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

    -- | Attempt to convert an 'Integral' type @a@ to an 'Integral' type @b@ using
    -- the size of the types as measured by 'Bits' methods.
    --
    -- A simpler version of this function is:
    --
    -- > toIntegral :: (Integral a, Integral b) => a -> Maybe b
    -- > toIntegral x
    -- >   | toInteger x == y = Just (fromInteger y)
    -- >   | otherwise        = Nothing
    -- >   where
    -- >     y = toInteger x
    --
    -- This version requires going through 'Integer', which can be inefficient.
    -- However, @toIntegralSized@ is optimized to allow GHC to statically determine
    -- the relative type sizes (as measured by 'bitSizeMaybe' and 'isSigned') and
    -- avoid going through 'Integer' for many types. (The implementation uses
    -- 'fromIntegral', which is itself optimized with rules for @base@ types but may
    -- go through 'Integer' for some type pairs.)
    --
    -- @since 4.8.0.0

    toIntegralSized :: (Integral a, Integral b, Bits a, Bits b) => a -> Maybe b
    toIntegralSized :: forall a b.
    (Integral a, Integral b, Bits a, Bits b) =>
    a -> Maybe b
    toIntegralSized a
    x                 -- See Note [toIntegralSized optimization]
      | forall b a. b -> (a -> b) -> Maybe a -> b
    maybe Bool
    True (forall a. Ord a => a -> a -> Bool
    <= a
    x) Maybe a
    yMinBound
      , forall b a. b -> (a -> b) -> Maybe a -> b
    maybe Bool
    True (a
    x forall a. Ord a => a -> a -> Bool
    <=) Maybe a
    yMaxBound = forall a. a -> Maybe a
    Just b
    y
      | Bool
    otherwise                   = forall a. Maybe a
    Nothing
      where
        y :: b
    y = forall a b. (Integral a, Num b) => a -> b
    fromIntegral a
    x

        xWidth :: Maybe Int
    xWidth = forall a. Bits a => a -> Maybe Int
    bitSizeMaybe a
    x
        yWidth :: Maybe Int
    yWidth = forall a. Bits a => a -> Maybe Int
    bitSizeMaybe b
    y

        yMinBound :: Maybe a
    yMinBound
          | forall a b. (Bits a, Bits b) => a -> b -> Bool
    isBitSubType a
    x b
    y = forall a. Maybe a
    Nothing
          | forall a. Bits a => a -> Bool
    isSigned a
    x, Bool -> Bool
    not (forall a. Bits a => a -> Bool
    isSigned b
    y) = forall a. a -> Maybe a
    Just a
    0
          | forall a. Bits a => a -> Bool
    isSigned a
    x, forall a. Bits a => a -> Bool
    isSigned b
    y
          , Just Int
    yW <- Maybe Int
    yWidth = forall a. a -> Maybe a
    Just (forall a. Num a => a -> a
    negate forall a b. (a -> b) -> a -> b
    $ forall a. Bits a => Int -> a
    bit (Int
    yWforall a. Num a => a -> a -> a
    -Int
    1)) -- Assumes sub-type
          | Bool
    otherwise = forall a. Maybe a
    Nothing

        yMaxBound :: Maybe a
    yMaxBound
          | forall a b. (Bits a, Bits b) => a -> b -> Bool
    isBitSubType a
    x b
    y = forall a. Maybe a
    Nothing
          | forall a. Bits a => a -> Bool
    isSigned a
    x, Bool -> Bool
    not (forall a. Bits a => a -> Bool
    isSigned b
    y)
          , Just Int
    xW <- Maybe Int
    xWidth, Just Int
    yW <- Maybe Int
    yWidth
          , Int
    xW forall a. Ord a => a -> a -> Bool
    <= Int
    yWforall a. Num a => a -> a -> a
    +Int
    1 = forall a. Maybe a
    Nothing -- Max bound beyond a's domain
          | Just Int
    yW <- Maybe Int
    yWidth = if forall a. Bits a => a -> Bool
    isSigned b
    y
                                then forall a. a -> Maybe a
    Just (forall a. Bits a => Int -> a
    bit (Int
    yWforall a. Num a => a -> a -> a
    -Int
    1)forall a. Num a => a -> a -> a
    -a
    1)
                                else forall a. a -> Maybe a
    Just (forall a. Bits a => Int -> a
    bit Int
    yWforall a. Num a => a -> a -> a
    -a
    1)
          | Bool
    otherwise = forall a. Maybe a
    Nothing
    {-# INLINABLE toIntegralSized #-}

    -- | 'True' if the size of @a@ is @<=@ the size of @b@, where size is measured
    -- by 'bitSizeMaybe' and 'isSigned'.
    isBitSubType :: (Bits a, Bits b) => a -> b -> Bool
    isBitSubType :: forall a b. (Bits a, Bits b) => a -> b -> Bool
    isBitSubType a
    x b
    y
      -- Reflexive
      | Maybe Int
    xWidth forall a. Eq a => a -> a -> Bool
    == Maybe Int
    yWidth, Bool
    xSigned forall a. Eq a => a -> a -> Bool
    == Bool
    ySigned = Bool
    True

      -- Every integer is a subset of 'Integer'
      | Bool
    ySigned, forall a. Maybe a
    Nothing forall a. Eq a => a -> a -> Bool
    == Maybe Int
    yWidth                  = Bool
    True
      | Bool -> Bool
    not Bool
    xSigned, Bool -> Bool
    not Bool
    ySigned, forall a. Maybe a
    Nothing forall a. Eq a => a -> a -> Bool
    == Maybe Int
    yWidth = Bool
    True

      -- Sub-type relations between fixed-with types
      | Bool
    xSigned forall a. Eq a => a -> a -> Bool
    == Bool
    ySigned,   Just Int
    xW <- Maybe Int
    xWidth, Just Int
    yW <- Maybe Int
    yWidth = Int
    xW forall a. Ord a => a -> a -> Bool
    <= Int
    yW
      | Bool -> Bool
    not Bool
    xSigned, Bool
    ySigned, Just Int
    xW <- Maybe Int
    xWidth, Just Int
    yW <- Maybe Int
    yWidth = Int
    xW forall a. Ord a => a -> a -> Bool
    <  Int
    yW

      | Bool
    otherwise = Bool
    False
      where
        xWidth :: Maybe Int
    xWidth  = forall a. Bits a => a -> Maybe Int
    bitSizeMaybe a
    x
        xSigned :: Bool
    xSigned = forall a. Bits a => a -> Bool
    isSigned     a
    x

        yWidth :: Maybe Int
    yWidth  = forall a. Bits a => a -> Maybe Int
    bitSizeMaybe b
    y
        ySigned :: Bool
    ySigned = forall a. Bits a => a -> Bool
    isSigned     b
    y
    {-# INLINE isBitSubType #-}

    {-      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
             }
    -}

    -- Note [toIntegralSized optimization]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -- The code in 'toIntegralSized' relies on GHC optimizing away statically
    -- decidable branches.
    --
    -- If both integral types are statically known, GHC will be able optimize the
    -- code significantly (for @-O1@ and better).
    --
    -- For instance (as of GHC 7.8.1) the following definitions:
    --
    -- > w16_to_i32 = toIntegralSized :: Word16 -> Maybe Int32
    -- >
    -- > i16_to_w16 = toIntegralSized :: Int16 -> Maybe Word16
    --
    -- are translated into the following (simplified) /GHC Core/ language:
    --
    -- > w16_to_i32 = \x -> Just (case x of _ { W16# x# -> I32# (word2Int# x#) })
    -- >
    -- > i16_to_w16 = \x -> case eta of _
    -- >   { I16# b1 -> case tagToEnum# (<=# 0 b1) of _
    -- >       { False -> Nothing
    -- >       ; True -> Just (W16# (narrow16Word# (int2Word# b1)))
    -- >       }
    -- >   }