Bits.hs

{-# LANGUAGE NoImplicitPrelude, CPP #-}
{-# OPTIONS_GHC -XNoImplicitPrelude #-}

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

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

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

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

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

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

#ifdef __HUGS__
import Hugs.Bits
#endif

#if defined(__UHC__)
#include "IntLikeInstance.h"

import UHC.Bits
import UHC.Real
import UHC.Base
#endif

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

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

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

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

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

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

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

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

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

    x `shift`   i | i<0       = x `shiftR` (-i)
                  | i>0       = x `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
    bit               :: Int -> a

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    {-# INLINE shiftR #-}
    -- same as the default definition, but we want it inlined (#2376)
    x `shiftR`  i = x `shift`  (-i)
#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
#elif defined(__UHC__)
    (.&.)                  = primAndInt
    (.|.)                  = primOrInt
    xor                    = primXorInt
    complement             = primComplementInt
    shiftL                 = primShiftLeftInt
    shiftR                 = primShiftRightInt
    rotateL                = primRotateLeftInt
    rotateR                = primRotateRightInt
#if defined( __UHC_TARGET_JS__ )
    bitSize  _             = 31 -- for now...
#elif defined( __UHC_TARGET_BC__ )
    bitSize _              = SIZEOF_HSINT*8 - BITSIZEOF_WORDTAG
#else
    bitSize _              = SIZEOF_HSINT*8
#endif
#endif /* __NHC__ , __UHC__ */

    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
#elif defined(__UHC__)
   (.&.) = primAndInteger
   (.|.) = primOrInteger
   xor = primXorInteger
   complement = primComplementInteger
#else
   -- reduce bitwise binary operations to special cases we can handle

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

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

#ifdef __UHC__
   shiftL = primShiftLeftInteger
   shiftR = primShiftRightInteger
#else
   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__) && !defined(__UHC__)
-- 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
         }
-}