content: {-# 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, -- :: 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
      unsafeShiftL, unsafeShiftR,  -- :: a -> Int -> a
      rotateL, rotateR,  -- :: a -> Int -> a
      popCount           -- :: a -> Int
    )
  
    -- 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.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 (Eq a, 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 `shiftL` i
                    | otherwise = 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 `rotate`  i | i<0       = x `rotateR` (-i)
                    | i>0       = x `rotateL` i
                    | otherwise = 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))
      -}
  
      -- | @bit i@ is a value with the @i@th bit set and all other bits clear
      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
  
      {-# INLINE bit #-}
      {-# INLINE setBit #-}
      {-# INLINE clearBit #-}
      {-# INLINE complementBit #-}
      {-# INLINE testBit #-}
      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
      {-# INLINE shiftL #-}
      x `shiftL`  i = x `shift`  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. -}
      unsafeShiftL            :: a -> Int -> a
      {-# INLINE unsafeShiftL #-}
      x `unsafeShiftL` i = x `shiftL` 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'.
  
          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 `shiftR`  i = x `shift`  (-i)
  
      {-| Shift the first argument right by the specified number of bits, which
          must be non-negative an 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. -}
      unsafeShiftR            :: a -> Int -> a
      {-# INLINE unsafeShiftR #-}
      x `unsafeShiftR` i = x `shiftR` 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 `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
      {-# INLINE rotateR #-}
      x `rotateR` i = x `rotate` (-i)
  
      {-| Return the number of set bits in the argument.  This number is
          known as the population count or the Hamming weight. -}
      popCount          :: a -> Int
      popCount = go 0
        where
          go !c 0 = c
          go c w = go (c+1) (w .&. (w - 1))  -- clear the least significant bit set
      {-# INLINABLE popCount #-}
      {- This implementation is intentionally naive.  Instances are
         expected to override it with something optimized for their
         size. -}
  
  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#)
      (I# x#) `shiftL` (I# i#) = I# (x# `iShiftL#` i#)
      (I# x#) `unsafeShiftL` (I# i#) = I# (x# `uncheckedIShiftL#` i#)
      (I# x#) `shiftR` (I# i#) = I# (x# `iShiftRA#` i#)
      (I# x#) `unsafeShiftR` (I# i#) = I# (x# `uncheckedIShiftRA#` 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
  
      popCount (I# x#) = I# (word2Int# (popCnt# (int2Word# x#)))
  
  #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
  #if defined(__GLASGOW_HASKELL__)
     (.&.) = andInteger
     (.|.) = orInteger
     xor = xorInteger
     complement = complementInteger
     shift x i@(I# i#) | i >= 0    = shiftLInteger x i#
                       | otherwise = shiftRInteger x (negateInt# i#)
  #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
     shift x i | i >= 0    = x * 2^i
               | otherwise = x `div` 2^(-i)
  #endif
  
     rotate x i = shift x i   -- since an Integer never wraps around
  
     bitSize _  = error "Data.Bits.bitSize(Integer)"
     isSigned _ = True
  
  #if !defined(__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
           }
  -} 
  
  