{-# OPTIONS_GHC -fno-implicit-prelude #-} ----------------------------------------------------------------------------- -- | -- 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__) #include "MachDeps.h" #endif #ifdef __GLASGOW_HASKELL__ import GHC.Num import GHC.Real 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 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 | i>0 = x `shiftL` i {-| @'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 | i>0 = x `rotateL` i {- -- 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 #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 #ifdef __GLASGOW_HASKELL__ (S# x) .&. (S# y) = S# (word2Int# (int2Word# x `and#` int2Word# y)) x@(S# _) .&. y = toBig x .&. y x .&. y@(S# _) = x .&. toBig y (J# s1 d1) .&. (J# s2 d2) = case andInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d (S# x) .|. (S# y) = S# (word2Int# (int2Word# x `or#` int2Word# y)) x@(S# _) .|. y = toBig x .|. y x .|. y@(S# _) = x .|. toBig y (J# s1 d1) .|. (J# s2 d2) = case orInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d (S# x) `xor` (S# y) = S# (word2Int# (int2Word# x `xor#` int2Word# y)) x@(S# _) `xor` y = toBig x `xor` y x `xor` y@(S# _) = x `xor` toBig y (J# s1 d1) `xor` (J# s2 d2) = case xorInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d complement (S# x) = S# (word2Int# (int2Word# x `xor#` int2Word# (0# -# 1#))) complement (J# s d) = case complementInteger# s d of (# s, d #) -> J# s d #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 shift x i | i >= 0 = x * 2^i | otherwise = x `div` 2^(-i) rotate x i = shift x i -- since an Integer never wraps around bitSize _ = error "Data.Bits.bitSize(Integer)" isSigned _ = True #ifndef __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 } -}