Data/Bits.hs

{-# 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
 ),

 bitDefault,
 testBitDefault,
 popCountDefault
 -- 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.Enum
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', 'isSigned', 'testBit', 'bit', and 'popCount'. The latter three can
be implemented using `testBitDefault', 'bitDefault, and 'popCountDefault', if
@a@ is also an instance of 'Num'.
-}
class Eq 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 setBit #-}
 {-# INLINE clearBit #-}
 {-# INLINE complementBit #-}
 x `setBit` i = x .|. bit i
 x `clearBit` i = x .&. complement (bit i)
 x `complementBit` i = x `xor` bit i

 {-| 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

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

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

-- | Default implementation for 'popCount'.
--
-- This implementation is intentionally naive. Instances are expected to provide
-- an optimized implementation for their size.
popCountDefault :: (Bits a, Num a) => a -> Int
popCountDefault = go 0
 where
 go !c 0 = c
 go c w = go (c+1) (w .&. (w - 1)) -- clear the least significant
{-# INLINABLE popCountDefault #-}

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

#ifdef __GLASGOW_HASKELL__
 bit = bitDefault

 testBit = testBitDefault

 (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__ */

 popCount = popCountDefault

#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
 bit = bitDefault
 testBit = testBitDefault
 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__ */

#if defined(__GLASGOW_HASKELL__)
instance Bits Word where
 {-# INLINE shift #-}
 {-# INLINE bit #-}
 {-# INLINE testBit #-}

 (W# x#) .&. (W# y#) = W# (x# `and#` y#)
 (W# x#) .|. (W# y#) = W# (x# `or#` y#)
 (W# x#) `xor` (W# y#) = W# (x# `xor#` y#)
 complement (W# x#) = W# (x# `xor#` mb#)
 where !(W# mb#) = maxBound
 (W# x#) `shift` (I# i#)
 | i# >=# 0# = W# (x# `shiftL#` i#)
 | otherwise = W# (x# `shiftRL#` negateInt# i#)
 (W# x#) `shiftL` (I# i#) = W# (x# `shiftL#` i#)
 (W# x#) `unsafeShiftL` (I# i#) = W# (x# `uncheckedShiftL#` i#)
 (W# x#) `shiftR` (I# i#) = W# (x# `shiftRL#` i#)
 (W# x#) `unsafeShiftR` (I# i#) = W# (x# `uncheckedShiftRL#` i#)
 (W# x#) `rotate` (I# i#)
 | i'# ==# 0# = W# x#
 | otherwise = W# ((x# `uncheckedShiftL#` i'#) `or#` (x# `uncheckedShiftRL#` (wsib -# i'#)))
 where
 !i'# = word2Int# (int2Word# i# `and#` int2Word# (wsib -# 1#))
 !wsib = WORD_SIZE_IN_BITS# {- work around preprocessor problem (??) -}
 bitSize _ = WORD_SIZE_IN_BITS
 isSigned _ = False
 popCount (W# x#) = I# (word2Int# (popCnt# x#))
 bit = bitDefault
 testBit = testBitDefault
#endif

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

 bit = bitDefault
 testBit = testBitDefault
 popCount = popCountDefault

 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
 }
-}