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

-----------------------------------------------------------------------------
-- |
-- 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,
    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.Enum
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

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

    x :: a
x `rotate`  i :: Int
i | Int
iInt -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<0       = a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`rotateR` (-Int
i)
                  | Int
iInt -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>0       = a
x a -> Int -> a
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 = a -> Int -> a
forall a. Bits a => a -> Int -> a
clearBit (Int -> a
forall a. Bits a => Int -> a
bit 0) 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

    -- | Return 'True' if the @n@th bit of the argument is 1
    --
    -- 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 b :: a
b = Int -> Maybe Int -> Int
forall a. a -> Maybe a -> a
fromMaybe ([Char] -> Int
forall a. HasCallStack => [Char] -> a
error "bitSize is undefined") (a -> Maybe Int
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 #-}
    x :: a
x `setBit` i :: Int
i        = a
x a -> a -> a
forall a. Bits a => a -> a -> a
.|. Int -> a
forall a. Bits a => Int -> a
bit Int
i
    x :: a
x `clearBit` i :: Int
i      = a
x a -> a -> a
forall a. Bits a => a -> a -> a
.&. a -> a
forall a. Bits a => a -> a
complement (Int -> a
forall a. Bits a => Int -> a
bit Int
i)
    x :: a
x `complementBit` i :: Int
i = a
x a -> a -> a
forall a. Bits a => a -> a -> a
`xor` Int -> a
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 #-}
    x :: a
x `shiftL`  i :: Int
i = a
x a -> Int -> a
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 #-}
    x :: a
x `unsafeShiftL` i :: Int
i = a
x a -> Int -> a
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 #-}
    x :: a
x `shiftR`  i :: Int
i = a
x a -> Int -> a
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 #-}
    x :: a
x `unsafeShiftR` i :: Int
i = a
x a -> Int -> a
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 #-}
    x :: a
x `rotateL` i :: Int
i = a
x a -> Int -> a
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 #-}
    x :: a
x `rotateR` i :: Int
i = a
x a -> Int -> a
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 x :: b
x = (Int
wInt -> Int -> Int
forall a. Num a => a -> a -> a
-1) Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int -> Int
go (Int
wInt -> Int -> Int
forall a. Num a => a -> a -> a
-1)
      where
        go :: Int -> Int
go i :: Int
i | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< 0       = Int
i -- no bit set
             | b -> Int -> Bool
forall a. Bits a => a -> Int -> Bool
testBit b
x Int
i = Int
i
             | Bool
otherwise   = Int -> Int
go (Int
iInt -> Int -> Int
forall a. Num a => a -> a -> a
-1)

        w :: Int
w = b -> Int
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 x :: b
x = Int -> Int
go 0
      where
        go :: Int -> Int
go i :: Int
i | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
w      = Int
i
             | b -> Int -> Bool
forall a. Bits a => a -> Int -> Bool
testBit b
x Int
i = Int
i
             | Bool
otherwise   = Int -> Int
go (Int
iInt -> Int -> Int
forall a. Num a => a -> a -> a
+1)

        w :: Int
w = b -> Int
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 :: Int -> a
bitDefault = \i :: Int
i -> 1 a -> Int -> a
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 :: a -> Int -> Bool
testBitDefault = \x :: a
x i :: Int
i -> (a
x a -> a -> a
forall a. Bits a => a -> a -> a
.&. Int -> a
forall a. Bits a => Int -> a
bit Int
i) a -> a -> Bool
forall a. Eq a => a -> a -> Bool
/= 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 :: a -> Int
popCountDefault = Int -> a -> Int
forall t t. (Num t, Num t, Bits t) => t -> t -> t
go 0
 where
   go :: t -> t -> t
go !t
c 0 = t
c
   go c :: t
c w :: t
w = t -> t -> t
go (t
ct -> t -> t
forall a. Num a => a -> a -> a
+1) (t
w t -> t -> t
forall a. Bits a => a -> a -> a
.&. (t
w t -> t -> t
forall a. Num a => a -> a -> a
- 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 = Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
(/=)

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

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

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

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

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

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

    bitSize :: Bool -> Int
bitSize _ = 1

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

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

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

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

    zeroBits :: Int
zeroBits = 0

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

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

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

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

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

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

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

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

    (W# x# :: Word#
x#) .&. :: Word -> Word -> Word
.&.   (W# y# :: Word#
y#)    = Word# -> Word
W# (Word#
x# Word# -> Word# -> Word#
`and#` Word#
y#)
    (W# x# :: Word#
x#) .|. :: Word -> Word -> Word
.|.   (W# y# :: Word#
y#)    = Word# -> Word
W# (Word#
x# Word# -> Word# -> Word#
`or#`  Word#
y#)
    (W# x# :: Word#
x#) xor :: Word -> Word -> Word
`xor` (W# y# :: Word#
y#)    = Word# -> Word
W# (Word#
x# Word# -> Word# -> Word#
`xor#` Word#
y#)
    complement :: Word -> Word
complement (W# x# :: Word#
x#)       = Word# -> Word
W# (Word#
x# Word# -> Word# -> Word#
`xor#` Word#
mb#)
        where !(W# mb# :: Word#
mb#) = Word
forall a. Bounded a => a
maxBound
    (W# x# :: Word#
x#) shift :: Word -> Int -> Word
`shift` (I# i# :: Int#
i#)
        | Int# -> Bool
isTrue# (Int#
i# 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# x# :: Word#
x#) shiftL :: Word -> Int -> Word
`shiftL` (I# i# :: Int#
i#)
        | Int# -> Bool
isTrue# (Int#
i# Int# -> Int# -> Int#
>=# 0#)      = Word# -> Word
W# (Word#
x# Word# -> Int# -> Word#
`shiftL#` Int#
i#)
        | Bool
otherwise                = Word
forall a. a
overflowError
    (W# x# :: Word#
x#) unsafeShiftL :: Word -> Int -> Word
`unsafeShiftL` (I# i# :: Int#
i#) = Word# -> Word
W# (Word#
x# Word# -> Int# -> Word#
`uncheckedShiftL#` Int#
i#)
    (W# x# :: Word#
x#) shiftR :: Word -> Int -> Word
`shiftR` (I# i# :: Int#
i#)
        | Int# -> Bool
isTrue# (Int#
i# Int# -> Int# -> Int#
>=# 0#)      = Word# -> Word
W# (Word#
x# Word# -> Int# -> Word#
`shiftRL#` Int#
i#)
        | Bool
otherwise                = Word
forall a. a
overflowError
    (W# x# :: Word#
x#) unsafeShiftR :: Word -> Int -> Word
`unsafeShiftR` (I# i# :: Int#
i#) = Word# -> Word
W# (Word#
x# Word# -> Int# -> Word#
`uncheckedShiftRL#` Int#
i#)
    (W# x# :: Word#
x#) rotate :: Word -> Int -> Word
`rotate` (I# i# :: Int#
i#)
        | Int# -> Bool
isTrue# (Int#
i'# 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#
-# 1#)
        !wsib :: Int#
wsib = WORD_SIZE_IN_BITS#  {- work around preprocessor problem (??) -}
    bitSizeMaybe :: Word -> Maybe Int
bitSizeMaybe i :: Word
i           = Int -> Maybe Int
forall a. a -> Maybe a
Just (Word -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize Word
i)
    bitSize :: Word -> Int
bitSize i :: Word
i                = Word -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize Word
i
    isSigned :: Word -> Bool
isSigned _               = Bool
False
    popCount :: Word -> Int
popCount (W# x# :: Word#
x#)         = Int# -> Int
I# (Word# -> Int#
word2Int# (Word# -> Word#
popCnt# Word#
x#))
    bit :: Int -> Word
bit                      = Int -> Word
forall a. (Bits a, Num a) => Int -> a
bitDefault
    testBit :: Word -> Int -> Bool
testBit                  = Word -> Int -> Bool
forall a. (Bits a, Num a) => a -> Int -> Bool
testBitDefault

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

-- | @since 2.01
instance Bits Integer where
   .&. :: Integer -> Integer -> Integer
(.&.) = Integer -> Integer -> Integer
andInteger
   .|. :: Integer -> Integer -> Integer
(.|.) = Integer -> Integer -> Integer
orInteger
   xor :: Integer -> Integer -> Integer
xor = Integer -> Integer -> Integer
xorInteger
   complement :: Integer -> Integer
complement = Integer -> Integer
complementInteger
   shift :: Integer -> Int -> Integer
shift x :: Integer
x i :: Int
i@(I# i# :: Int#
i#) | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= 0    = Integer -> Int# -> Integer
shiftLInteger Integer
x Int#
i#
                     | Bool
otherwise = Integer -> Int# -> Integer
shiftRInteger Integer
x (Int# -> Int#
negateInt# Int#
i#)
   testBit :: Integer -> Int -> Bool
testBit x :: Integer
x (I# i :: Int#
i) = Integer -> Int# -> Bool
testBitInteger Integer
x Int#
i
   zeroBits :: Integer
zeroBits   = 0

   bit :: Int -> Integer
bit (I# i# :: Int#
i#) = Int# -> Integer
bitInteger Int#
i#
   popCount :: Integer -> Int
popCount x :: Integer
x  = Int# -> Int
I# (Integer -> Int#
popCountInteger Integer
x)

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

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

-- | @since 4.8.0
instance Bits Natural where
   .&. :: Natural -> Natural -> Natural
(.&.) = Natural -> Natural -> Natural
andNatural
   .|. :: Natural -> Natural -> Natural
(.|.) = Natural -> Natural -> Natural
orNatural
   xor :: Natural -> Natural -> Natural
xor = Natural -> Natural -> Natural
xorNatural
   complement :: Natural -> Natural
complement _ = [Char] -> Natural
forall a. [Char] -> a
errorWithoutStackTrace
                    "Bits.complement: Natural complement undefined"
   shift :: Natural -> Int -> Natural
shift x :: Natural
x i :: Int
i
     | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= 0    = Natural -> Int -> Natural
shiftLNatural Natural
x Int
i
     | Bool
otherwise = Natural -> Int -> Natural
shiftRNatural Natural
x (Int -> Int
forall a. Num a => a -> a
negate Int
i)
   testBit :: Natural -> Int -> Bool
testBit x :: Natural
x i :: Int
i   = Natural -> Int -> Bool
testBitNatural Natural
x Int
i
   zeroBits :: Natural
zeroBits      = Word# -> Natural
wordToNaturalBase 0##
   clearBit :: Natural -> Int -> Natural
clearBit x :: Natural
x i :: Int
i  = Natural
x Natural -> Natural -> Natural
forall a. Bits a => a -> a -> a
`xor` (Int -> Natural
forall a. Bits a => Int -> a
bit Int
i Natural -> Natural -> Natural
forall a. Bits a => a -> a -> a
.&. Natural
x)

   bit :: Int -> Natural
bit (I# i# :: Int#
i#) = Int# -> Natural
bitNatural Int#
i#
   popCount :: Natural -> Int
popCount x :: Natural
x  = Natural -> Int
popCountNatural Natural
x

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

   bitSizeMaybe :: Natural -> Maybe Int
bitSizeMaybe _ = Maybe Int
forall a. Maybe a
Nothing
   bitSize :: Natural -> Int
bitSize _  = [Char] -> Int
forall a. [Char] -> a
errorWithoutStackTrace "Data.Bits.bitSize(Natural)"
   isSigned :: Natural -> Bool
isSigned _ = 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 :: a -> Maybe b
toIntegralSized x :: a
x                 -- See Note [toIntegralSized optimization]
  | Bool -> (a -> Bool) -> Maybe a -> Bool
forall b a. b -> (a -> b) -> Maybe a -> b
maybe Bool
True (a -> a -> Bool
forall a. Ord a => a -> a -> Bool
<= a
x) Maybe a
yMinBound
  , Bool -> (a -> Bool) -> Maybe a -> Bool
forall b a. b -> (a -> b) -> Maybe a -> b
maybe Bool
True (a
x a -> a -> Bool
forall a. Ord a => a -> a -> Bool
<=) Maybe a
yMaxBound = b -> Maybe b
forall a. a -> Maybe a
Just b
y
  | Bool
otherwise                   = Maybe b
forall a. Maybe a
Nothing
  where
    y :: b
y = a -> b
forall a b. (Integral a, Num b) => a -> b
fromIntegral a
x

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

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

    yMaxBound :: Maybe a
yMaxBound
      | a -> b -> Bool
forall a b. (Bits a, Bits b) => a -> b -> Bool
isBitSubType a
x b
y = Maybe a
forall a. Maybe a
Nothing
      | a -> Bool
forall a. Bits a => a -> Bool
isSigned a
x, Bool -> Bool
not (b -> Bool
forall a. Bits a => a -> Bool
isSigned b
y)
      , Just xW :: Int
xW <- Maybe Int
xWidth, Just yW :: Int
yW <- Maybe Int
yWidth
      , Int
xW Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<= Int
yWInt -> Int -> Int
forall a. Num a => a -> a -> a
+1 = Maybe a
forall a. Maybe a
Nothing -- Max bound beyond a's domain
      | Just yW :: Int
yW <- Maybe Int
yWidth = if b -> Bool
forall a. Bits a => a -> Bool
isSigned b
y
                            then a -> Maybe a
forall a. a -> Maybe a
Just (Int -> a
forall a. Bits a => Int -> a
bit (Int
yWInt -> Int -> Int
forall a. Num a => a -> a -> a
-1)a -> a -> a
forall a. Num a => a -> a -> a
-1)
                            else a -> Maybe a
forall a. a -> Maybe a
Just (Int -> a
forall a. Bits a => Int -> a
bit Int
yWa -> a -> a
forall a. Num a => a -> a -> a
-1)
      | Bool
otherwise = Maybe a
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 :: a -> b -> Bool
isBitSubType x :: a
x y :: b
y
  -- Reflexive
  | Maybe Int
xWidth Maybe Int -> Maybe Int -> Bool
forall a. Eq a => a -> a -> Bool
== Maybe Int
yWidth, Bool
xSigned Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
== Bool
ySigned = Bool
True

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

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

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

    yWidth :: Maybe Int
yWidth  = b -> Maybe Int
forall a. Bits a => a -> Maybe Int
bitSizeMaybe b
y
    ySigned :: Bool
ySigned = b -> Bool
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)))
-- >       }
-- >   }