{-# 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), bitDefault, testBitDefault, popCountDefault ) 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 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. 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)) -} -- | '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 = clearBit (bit 0) 0 -- | @bit /i/@ is a value with the @/i/@th bit set and all other bits clear. -- -- 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 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'. -} 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. /Since: 4.5.0.0/ -} 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. /Since: 4.5.0.0/ -} 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. /Since: 4.5.0.0/ -} popCount :: a -> Int {-# MINIMAL (.&.), (.|.), xor, complement, (shift | (shiftL, shiftR)), (rotate | (rotateL, rotateR)), bitSize, bitSizeMaybe, isSigned, testBit, bit, popCount #-} -- |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 -- 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 = \i -> 1 `shiftL` 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 = \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. -- -- /Since: 4.6.0.0/ 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 #-} -- Interpret 'Bool' as 1-bit bit-field; /Since: 4.7.0.0/ instance Bits Bool where (.&.) = (&&) (.|.) = (||) xor = (/=) complement = not shift x 0 = x shift _ _ = False rotate x _ = x bit 0 = True bit _ = False testBit x 0 = x testBit _ _ = False bitSizeMaybe _ = Just 1 bitSize _ = 1 isSigned _ = False popCount False = 0 popCount True = 1 instance FiniteBits Bool where finiteBitSize _ = 1 instance Bits Int where {-# INLINE shift #-} {-# INLINE bit #-} {-# INLINE testBit #-} zeroBits = 0 bit = bitDefault testBit = testBitDefault (I# x#) .&. (I# y#) = I# (x# `andI#` y#) (I# x#) .|. (I# y#) = I# (x# `orI#` y#) (I# x#) `xor` (I# y#) = I# (x# `xorI#` y#) complement (I# x#) = I# (notI# x#) (I# x#) `shift` (I# i#) | isTrue# (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# ((x# `uncheckedIShiftL#` i'#) `orI#` (x# `uncheckedIShiftRL#` (wsib -# i'#))) where !i'# = i# `andI#` (wsib -# 1#) !wsib = WORD_SIZE_IN_BITS# {- work around preprocessor problem (??) -} bitSizeMaybe i = Just (finiteBitSize i) bitSize i = finiteBitSize i popCount (I# x#) = I# (word2Int# (popCnt# (int2Word# x#))) isSigned _ = True instance FiniteBits Int where finiteBitSize _ = WORD_SIZE_IN_BITS 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#) | isTrue# (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#) | isTrue# (i'# ==# 0#) = W# x# | otherwise = W# ((x# `uncheckedShiftL#` i'#) `or#` (x# `uncheckedShiftRL#` (wsib -# i'#))) where !i'# = i# `andI#` (wsib -# 1#) !wsib = WORD_SIZE_IN_BITS# {- work around preprocessor problem (??) -} bitSizeMaybe i = Just (finiteBitSize i) bitSize i = finiteBitSize i isSigned _ = False popCount (W# x#) = I# (word2Int# (popCnt# x#)) bit = bitDefault testBit = testBitDefault instance FiniteBits Word where finiteBitSize _ = WORD_SIZE_IN_BITS instance Bits Integer where (.&.) = andInteger (.|.) = orInteger xor = xorInteger complement = complementInteger shift x i@(I# i#) | i >= 0 = shiftLInteger x i# | otherwise = shiftRInteger x (negateInt# i#) testBit x (I# i) = testBitInteger x i zeroBits = 0 bit = bitDefault popCount = popCountDefault rotate x i = shift x i -- since an Integer never wraps around bitSizeMaybe _ = Nothing bitSize _ = error "Data.Bits.bitSize(Integer)" isSigned _ = True {- 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 } -}