1 {-# OPTIONS_GHC -XNoImplicitPrelude #-}
2 -----------------------------------------------------------------------------
5 -- Copyright : (c) The University of Glasgow 2001
6 -- License : BSD-style (see the file libraries/base/LICENSE)
8 -- Maintainer : libraries@haskell.org
9 -- Stability : experimental
10 -- Portability : portable
12 -- This module defines bitwise operations for signed and unsigned
13 -- integers. Instances of the class 'Bits' for the 'Int' and
14 -- 'Integer' types are available from this module, and instances for
15 -- explicitly sized integral types are available from the
16 -- "Data.Int" and "Data.Word" modules.
18 -----------------------------------------------------------------------------
22 (.&.), (.|.), xor, -- :: a -> a -> a
23 complement, -- :: a -> a
24 shift, -- :: a -> Int -> a
25 rotate, -- :: a -> Int -> a
27 setBit, -- :: a -> Int -> a
28 clearBit, -- :: a -> Int -> a
29 complementBit, -- :: a -> Int -> a
30 testBit, -- :: a -> Int -> Bool
31 bitSize, -- :: a -> Int
32 isSigned, -- :: a -> Bool
33 shiftL, shiftR, -- :: a -> Int -> a
34 rotateL, rotateR -- :: a -> Int -> a
38 -- instance Bits Integer
41 -- Defines the @Bits@ class containing bit-based operations.
42 -- See library document for details on the semantics of the
43 -- individual operations.
45 #if defined(__GLASGOW_HASKELL__) || defined(__HUGS__)
49 #ifdef __GLASGOW_HASKELL__
58 infixl 8 `shift`, `rotate`, `shiftL`, `shiftR`, `rotateL`, `rotateR`
64 The 'Bits' class defines bitwise operations over integral types.
66 * Bits are numbered from 0 with bit 0 being the least
69 Minimal complete definition: '.&.', '.|.', 'xor', 'complement',
70 ('shift' or ('shiftL' and 'shiftR')), ('rotate' or ('rotateL' and 'rotateR')),
71 'bitSize' and 'isSigned'.
73 class Num a => Bits a where
83 {-| Reverse all the bits in the argument -}
86 {-| @'shift' x i@ shifts @x@ left by @i@ bits if @i@ is positive,
87 or right by @-i@ bits otherwise.
88 Right shifts perform sign extension on signed number types;
89 i.e. they fill the top bits with 1 if the @x@ is negative
92 An instance can define either this unified 'shift' or 'shiftL' and
93 'shiftR', depending on which is more convenient for the type in
95 shift :: a -> Int -> a
97 x `shift` i | i<0 = x `shiftR` (-i)
101 {-| @'rotate' x i@ rotates @x@ left by @i@ bits if @i@ is positive,
102 or right by @-i@ bits otherwise.
104 For unbounded types like 'Integer', 'rotate' is equivalent to 'shift'.
106 An instance can define either this unified 'rotate' or 'rotateL' and
107 'rotateR', depending on which is more convenient for the type in
109 rotate :: a -> Int -> a
111 x `rotate` i | i<0 = x `rotateR` (-i)
112 | i>0 = x `rotateL` i
116 -- Rotation can be implemented in terms of two shifts, but care is
117 -- needed for negative values. This suggested implementation assumes
118 -- 2's-complement arithmetic. It is commented out because it would
119 -- require an extra context (Ord a) on the signature of 'rotate'.
120 x `rotate` i | i<0 && isSigned x && x<0
121 = let left = i+bitSize x in
122 ((x `shift` i) .&. complement ((-1) `shift` left))
124 | i<0 = (x `shift` i) .|. (x `shift` (i+bitSize x))
126 | i>0 = (x `shift` i) .|. (x `shift` (i-bitSize x))
129 -- | @bit i@ is a value with the @i@th bit set
132 -- | @x \`setBit\` i@ is the same as @x .|. bit i@
133 setBit :: a -> Int -> a
135 -- | @x \`clearBit\` i@ is the same as @x .&. complement (bit i)@
136 clearBit :: a -> Int -> a
138 -- | @x \`complementBit\` i@ is the same as @x \`xor\` bit i@
139 complementBit :: a -> Int -> a
141 -- | Return 'True' if the @n@th bit of the argument is 1
142 testBit :: a -> Int -> Bool
144 {-| Return the number of bits in the type of the argument. The actual
145 value of the argument is ignored. The function 'bitSize' is
146 undefined for types that do not have a fixed bitsize, like 'Integer'.
150 {-| Return 'True' if the argument is a signed type. The actual
151 value of the argument is ignored -}
152 isSigned :: a -> Bool
155 x `setBit` i = x .|. bit i
156 x `clearBit` i = x .&. complement (bit i)
157 x `complementBit` i = x `xor` bit i
158 x `testBit` i = (x .&. bit i) /= 0
160 {-| Shift the argument left by the specified number of bits
161 (which must be non-negative).
163 An instance can define either this and 'shiftR' or the unified
164 'shift', depending on which is more convenient for the type in
166 shiftL :: a -> Int -> a
167 x `shiftL` i = x `shift` i
169 {-| Shift the first argument right by the specified number of bits
170 (which must be non-negative).
171 Right shifts perform sign extension on signed number types;
172 i.e. they fill the top bits with 1 if the @x@ is negative
173 and with 0 otherwise.
175 An instance can define either this and 'shiftL' or the unified
176 'shift', depending on which is more convenient for the type in
178 shiftR :: a -> Int -> a
179 x `shiftR` i = x `shift` (-i)
181 {-| Rotate the argument left by the specified number of bits
182 (which must be non-negative).
184 An instance can define either this and 'rotateR' or the unified
185 'rotate', depending on which is more convenient for the type in
187 rotateL :: a -> Int -> a
188 x `rotateL` i = x `rotate` i
190 {-| Rotate the argument right by the specified number of bits
191 (which must be non-negative).
193 An instance can define either this and 'rotateL' or the unified
194 'rotate', depending on which is more convenient for the type in
196 rotateR :: a -> Int -> a
197 x `rotateR` i = x `rotate` (-i)
199 instance Bits Int where
202 #ifdef __GLASGOW_HASKELL__
203 (I# x#) .&. (I# y#) = I# (word2Int# (int2Word# x# `and#` int2Word# y#))
205 (I# x#) .|. (I# y#) = I# (word2Int# (int2Word# x# `or#` int2Word# y#))
207 (I# x#) `xor` (I# y#) = I# (word2Int# (int2Word# x# `xor#` int2Word# y#))
209 complement (I# x#) = I# (word2Int# (int2Word# x# `xor#` int2Word# (-1#)))
211 (I# x#) `shift` (I# i#)
212 | i# >=# 0# = I# (x# `iShiftL#` i#)
213 | otherwise = I# (x# `iShiftRA#` negateInt# i#)
215 {-# INLINE rotate #-} -- See Note [Constant folding for rotate]
216 (I# x#) `rotate` (I# i#) =
217 I# (word2Int# ((x'# `uncheckedShiftL#` i'#) `or#`
218 (x'# `uncheckedShiftRL#` (wsib -# i'#))))
221 !i'# = word2Int# (int2Word# i# `and#` int2Word# (wsib -# 1#))
222 !wsib = WORD_SIZE_IN_BITS# {- work around preprocessor problem (??) -}
223 bitSize _ = WORD_SIZE_IN_BITS
225 {-# INLINE shiftR #-}
226 -- same as the default definition, but we want it inlined (#2376)
227 x `shiftR` i = x `shift` (-i)
228 #else /* !__GLASGOW_HASKELL__ */
234 complement = primComplementInt
237 testBit = primTestInt
238 bitSize _ = SIZEOF_HSINT*8
239 #elif defined(__NHC__)
240 (.&.) = nhc_primIntAnd
241 (.|.) = nhc_primIntOr
243 complement = nhc_primIntCompl
244 shiftL = nhc_primIntLsh
245 shiftR = nhc_primIntRsh
250 | i<0 && x<0 = let left = i+bitSize x in
251 ((x `shift` i) .&. complement ((-1) `shift` left))
253 | i<0 = (x `shift` i) .|. (x `shift` (i+bitSize x))
255 | i>0 = (x `shift` i) .|. (x `shift` (i-bitSize x))
257 #endif /* !__GLASGOW_HASKELL__ */
262 foreign import ccall nhc_primIntAnd :: Int -> Int -> Int
263 foreign import ccall nhc_primIntOr :: Int -> Int -> Int
264 foreign import ccall nhc_primIntXor :: Int -> Int -> Int
265 foreign import ccall nhc_primIntLsh :: Int -> Int -> Int
266 foreign import ccall nhc_primIntRsh :: Int -> Int -> Int
267 foreign import ccall nhc_primIntCompl :: Int -> Int
270 instance Bits Integer where
271 #if defined(__GLASGOW_HASKELL__)
275 complement = complementInteger
276 shift x i@(I# i#) | i >= 0 = shiftLInteger x i#
277 | otherwise = shiftRInteger x (negateInt# i#)
279 -- reduce bitwise binary operations to special cases we can handle
281 x .&. y | x<0 && y<0 = complement (complement x `posOr` complement y)
282 | otherwise = x `posAnd` y
284 x .|. y | x<0 || y<0 = complement (complement x `posAnd` complement y)
285 | otherwise = x `posOr` y
287 x `xor` y | x<0 && y<0 = complement x `posXOr` complement y
288 | x<0 = complement (complement x `posXOr` y)
289 | y<0 = complement (x `posXOr` complement y)
290 | otherwise = x `posXOr` y
292 -- assuming infinite 2's-complement arithmetic
293 complement a = -1 - a
294 shift x i | i >= 0 = x * 2^i
295 | otherwise = x `div` 2^(-i)
298 rotate x i = shift x i -- since an Integer never wraps around
300 bitSize _ = error "Data.Bits.bitSize(Integer)"
303 #if !defined(__GLASGOW_HASKELL__)
304 -- Crude implementation of bitwise operations on Integers: convert them
305 -- to finite lists of Ints (least significant first), zip and convert
308 -- posAnd requires at least one argument non-negative
309 -- posOr and posXOr require both arguments non-negative
311 posAnd, posOr, posXOr :: Integer -> Integer -> Integer
312 posAnd x y = fromInts $ zipWith (.&.) (toInts x) (toInts y)
313 posOr x y = fromInts $ longZipWith (.|.) (toInts x) (toInts y)
314 posXOr x y = fromInts $ longZipWith xor (toInts x) (toInts y)
316 longZipWith :: (a -> a -> a) -> [a] -> [a] -> [a]
317 longZipWith f xs [] = xs
318 longZipWith f [] ys = ys
319 longZipWith f (x:xs) (y:ys) = f x y:longZipWith f xs ys
321 toInts :: Integer -> [Int]
324 | otherwise = mkInt (n `mod` numInts):toInts (n `div` numInts)
325 where mkInt n | n > toInteger(maxBound::Int) = fromInteger (n-numInts)
326 | otherwise = fromInteger n
328 fromInts :: [Int] -> Integer
329 fromInts = foldr catInt 0
330 where catInt d n = (if d<0 then n+1 else n)*numInts + toInteger d
332 numInts = toInteger (maxBound::Int) - toInteger (minBound::Int) + 1
333 #endif /* !__GLASGOW_HASKELL__ */
335 {- Note [Constant folding for rotate]
336 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
337 The INLINE on the Int instance of rotate enables it to be constant
339 sumU . mapU (`rotate` 3) . replicateU 10000000 $ (7 :: Int)
342 \ (ww_sO7 :: Int#) (ww1_sOb :: Int#) ->
343 case ww1_sOb of wild_XM {
344 __DEFAULT -> Main.$wfold (+# ww_sO7 56) (+# wild_XM 1);
346 whereas before it was left as a call to $wrotate.
348 All other Bits instances seem to inline well enough on their
349 own to enable constant folding; for example 'shift':
350 sumU . mapU (`shift` 3) . replicateU 10000000 $ (7 :: Int)
353 \ (ww_sOb :: Int#) (ww1_sOf :: Int#) ->
354 case ww1_sOf of wild_XM {
355 __DEFAULT -> Main.$wfold (+# ww_sOb 56) (+# wild_XM 1);