{-# 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.-------------------------------------------------------------------------------moduleData.Bits(Bits ((.&.) ,(.|.) ,xor ,complement ,shift ,rotate ,zeroBits ,bit ,setBit ,clearBit ,complementBit ,testBit ,bitSizeMaybe ,bitSize ,isSigned ,shiftL ,shiftR ,unsafeShiftL ,unsafeShiftR ,rotateL ,rotateR ,popCount ),FiniteBits (finiteBitSize ,countLeadingZeros ,countTrailingZeros ),bitDefault ,testBitDefault ,popCountDefault ,toIntegralSized )where-- Defines the @Bits@ class containing bit-based operations.-- See library document for details on the semantics of the-- individual operations.
#include "MachDeps.h"
importData.Maybe importGHC.Enum importGHC.Num importGHC.Base importGHC.Real infixl8`shift` ,`rotate` ,`shiftL` ,`shiftR` ,`rotateL` ,`rotateR` infixl7.&. infixl6`xor` infixl5.|. {-# DEPRECATEDbitSize"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.classEqa =>Bits a where{-# MINIMAL(.&.),(.|.),xor ,complement ,(shift |(shiftL ,shiftR )),(rotate |(rotateL ,rotateR )),bitSize ,bitSizeMaybe ,isSigned ,testBit ,bit ,popCount #-}-- | 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 :: a
x `shift` i :: Int
i |Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<0=a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`shiftR` (-Int
i )|Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>0=a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`shiftL` Int
i |Bool
otherwise =a
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 :: a
x `rotate` i :: Int
i |Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<0=a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`rotateR` (-Int
i )|Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>0=a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`rotateL` Int
i |Bool
otherwise =a
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 4.7.0.0zeroBits ::a zeroBits =a -> Int -> a
forall a. Bits a => a -> Int -> a
clearBit (Int -> a
forall a. Bits a => Int -> a
bit 0)0-- | @bit /i/@ is a value with the @/i/@th bit set and all other bits clear.---- Can be implemented using `bitDefault' if @a@ is also an-- instance of 'Num'.---- 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---- Can be implemented using `testBitDefault' if @a@ is also an-- instance of 'Num'.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'.
 Default implementation based upon 'bitSizeMaybe' provided since
 4.12.0.0.
 -}bitSize ::a ->IntbitSize b :: a
b =Int -> Maybe Int -> Int
forall a. a -> Maybe a -> a
fromMaybe ([Char] -> Int
forall a. HasCallStack => [Char] -> a
error "bitSize is undefined")(a -> Maybe Int
forall a. Bits a => a -> Maybe Int
bitSizeMaybe a
b ){-| Return 'True' if the argument is a signed type. The actual
 value of the argument is ignored -}isSigned ::a ->Bool{-# INLINEsetBit #-}{-# INLINEclearBit #-}{-# INLINEcomplementBit #-}x :: a
x `setBit` i :: Int
i =a
x a -> a -> a
forall a. Bits a => a -> a -> a
.|. Int -> a
forall a. Bits a => Int -> a
bit Int
i x :: a
x `clearBit` i :: Int
i =a
x a -> a -> a
forall a. Bits a => a -> a -> a
.&. a -> a
forall a. Bits a => a -> a
complement (Int -> a
forall a. Bits a => Int -> a
bit Int
i )x :: a
x `complementBit` i :: Int
i =a
x a -> a -> a
forall a. Bits a => a -> a -> a
`xor` Int -> a
forall a. Bits a => Int -> a
bit Int
i {-| Shift the argument left by the specified number of bits
 (which must be non-negative). Some instances may throw an
 'Control.Exception.Overflow' exception if given a negative input.
 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 {-# INLINEshiftL #-}x :: a
x `shiftL` i :: Int
i =a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`shift` Int
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 {-# INLINEunsafeShiftL #-}x :: a
x `unsafeShiftL` i :: Int
i =a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`shiftL` Int
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'. Some instances may throw an
 'Control.Exception.Overflow' exception if given a negative input.
 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 {-# INLINEshiftR #-}x :: a
x `shiftR` i :: Int
i =a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`shift` (-Int
i ){-| Shift the first argument right by the specified number of bits, which
 must be non-negative and 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 {-# INLINEunsafeShiftR #-}x :: a
x `unsafeShiftR` i :: Int
i =a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`shiftR` Int
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 {-# INLINErotateL #-}x :: a
x `rotateL` i :: Int
i =a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`rotate` Int
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 {-# INLINErotateR #-}x :: a
x `rotateR` i :: Int
i =a
x a -> Int -> a
forall a. Bits a => a -> Int -> a
`rotate` (-Int
i ){-| Return the number of set bits in the argument. This number is
 known as the population count or the Hamming weight.
 Can be implemented using `popCountDefault' if @a@ is also an
 instance of 'Num'.
 @since 4.5.0.0 -}popCount ::a ->Int-- |The 'FiniteBits' class denotes types with a finite, fixed number of bits.---- @since 4.7.0.0classBits 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 4.7.0.0finiteBitSize ::b ->Int-- | Count number of zero bits preceding the most significant set bit.---- @-- 'countLeadingZeros' ('zeroBits' :: a) = finiteBitSize ('zeroBits' :: a)-- @---- 'countLeadingZeros' can be used to compute log base 2 via---- @-- logBase2 x = 'finiteBitSize' x - 1 - 'countLeadingZeros' x-- @---- Note: The default implementation for this method is intentionally-- naive. However, the instances provided for the primitive-- integral types are implemented using CPU specific machine-- instructions.---- @since 4.8.0.0countLeadingZeros ::b ->IntcountLeadingZeros x :: b
x =(Int
w Int -> Int -> Int
forall a. Num a => a -> a -> a
- 1)Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int -> Int
go (Int
w Int -> Int -> Int
forall a. Num a => a -> a -> a
- 1)wherego :: Int -> Int
go i :: Int
i |Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<0=Int
i -- no bit set|b -> Int -> Bool
forall a. Bits a => a -> Int -> Bool
testBit b
x Int
i =Int
i |Bool
otherwise =Int -> Int
go (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- 1)w :: Int
w =b -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize b
x -- | Count number of zero bits following the least significant set bit.---- @-- 'countTrailingZeros' ('zeroBits' :: a) = finiteBitSize ('zeroBits' :: a)-- 'countTrailingZeros' . 'negate' = 'countTrailingZeros'-- @---- The related-- <http://en.wikipedia.org/wiki/Find_first_set find-first-set operation>-- can be expressed in terms of 'countTrailingZeros' as follows---- @-- findFirstSet x = 1 + 'countTrailingZeros' x-- @---- Note: The default implementation for this method is intentionally-- naive. However, the instances provided for the primitive-- integral types are implemented using CPU specific machine-- instructions.---- @since 4.8.0.0countTrailingZeros ::b ->IntcountTrailingZeros x :: b
x =Int -> Int
go 0wherego :: Int -> Int
go i :: Int
i |Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>=Int
w =Int
i |b -> Int -> Bool
forall a. Bits a => a -> Int -> Bool
testBit b
x Int
i =Int
i |Bool
otherwise =Int -> Int
go (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
+ 1)w :: Int
w =b -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize b
x -- 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 4.6.0.0bitDefault ::(Bits a ,Num a )=>Int->a bitDefault :: Int -> a
bitDefault =\i :: Int
i ->1a -> Int -> a
forall a. Bits a => a -> Int -> a
`shiftL` Int
i {-# INLINEbitDefault #-}-- | Default implementation for 'testBit'.---- Note that: @testBitDefault x i = (x .&. bit i) /= 0@---- @since 4.6.0.0testBitDefault ::(Bits a ,Num a )=>a ->Int->BooltestBitDefault :: a -> Int -> Bool
testBitDefault =\x :: a
x i :: Int
i ->(a
x a -> a -> a
forall a. Bits a => a -> a -> a
.&. Int -> a
forall a. Bits a => Int -> a
bit Int
i )a -> a -> Bool
forall a. Eq a => a -> a -> Bool
/=0{-# INLINEtestBitDefault #-}-- | Default implementation for 'popCount'.---- This implementation is intentionally naive. Instances are expected to provide-- an optimized implementation for their size.---- @since 4.6.0.0popCountDefault ::(Bits a ,Num a )=>a ->IntpopCountDefault :: a -> Int
popCountDefault =Int -> a -> Int
forall t t. (Num t, Num t, Bits t) => t -> t -> t
go 0wherego :: t -> t -> t
go !t
c 0=t
c go c :: t
c w :: t
w =t -> t -> t
go (t
c t -> t -> t
forall a. Num a => a -> a -> a
+ 1)(t
w t -> t -> t
forall a. Bits a => a -> a -> a
.&. (t
w t -> t -> t
forall a. Num a => a -> a -> a
- 1))-- clear the least significant{-# INLINABLEpopCountDefault #-}-- | Interpret 'Bool' as 1-bit bit-field---- @since 4.7.0.0instanceBits Boolwhere.&. :: Bool -> Bool -> Bool
(.&.) =Bool -> Bool -> Bool
(&&).|. :: Bool -> Bool -> Bool
(.|.) =Bool -> Bool -> Bool
(||)xor :: Bool -> Bool -> Bool
xor =Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
(/=)complement :: Bool -> Bool
complement =Bool -> Bool
notshift :: Bool -> Int -> Bool
shift x :: Bool
x 0=Bool
x shift __=Bool
Falserotate :: Bool -> Int -> Bool
rotate x :: Bool
x _=Bool
x bit :: Int -> Bool
bit 0=Bool
Truebit _=Bool
FalsetestBit :: Bool -> Int -> Bool
testBit x :: Bool
x 0=Bool
x testBit __=Bool
FalsebitSizeMaybe :: Bool -> Maybe Int
bitSizeMaybe _=Int -> Maybe Int
forall a. a -> Maybe a
Just 1bitSize :: Bool -> Int
bitSize _=1isSigned :: Bool -> Bool
isSigned _=Bool
FalsepopCount :: Bool -> Int
popCount False=0popCount True=1-- | @since 4.7.0.0instanceFiniteBits BoolwherefiniteBitSize :: Bool -> Int
finiteBitSize _=1countTrailingZeros :: Bool -> Int
countTrailingZeros x :: Bool
x =ifBool
x then0else1countLeadingZeros :: Bool -> Int
countLeadingZeros x :: Bool
x =ifBool
x then0else1-- | @since 2.01instanceBits Intwhere{-# INLINEshift #-}{-# INLINEbit #-}{-# INLINEtestBit #-}zeroBits :: Int
zeroBits =0bit :: Int -> Int
bit =Int -> Int
forall a. (Bits a, Num a) => Int -> a
bitDefault testBit :: Int -> Int -> Bool
testBit =Int -> Int -> Bool
forall a. (Bits a, Num a) => a -> Int -> Bool
testBitDefault (I#x# :: Int#
x# ).&. :: Int -> Int -> Int
.&. (I#y# :: Int#
y# )=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`andI#`Int#
y# )(I#x# :: Int#
x# ).|. :: Int -> Int -> Int
.|. (I#y# :: Int#
y# )=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`orI#`Int#
y# )(I#x# :: Int#
x# )xor :: Int -> Int -> Int
`xor` (I#y# :: Int#
y# )=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`xorI#`Int#
y# )complement :: Int -> Int
complement (I#x# :: Int#
x# )=Int# -> Int
I#(Int# -> Int#
notI#Int#
x# )(I#x# :: Int#
x# )shift :: Int -> Int -> Int
`shift` (I#i# :: Int#
i# )|Int# -> Bool
isTrue#(Int#
i# Int# -> Int# -> Int#
>=#0#)=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`iShiftL#` Int#
i# )|Bool
otherwise =Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`iShiftRA#` Int# -> Int#
negateInt#Int#
i# )(I#x# :: Int#
x# )shiftL :: Int -> Int -> Int
`shiftL` (I#i# :: Int#
i# )|Int# -> Bool
isTrue#(Int#
i# Int# -> Int# -> Int#
>=#0#)=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`iShiftL#` Int#
i# )|Bool
otherwise =Int
forall a. a
overflowError (I#x# :: Int#
x# )unsafeShiftL :: Int -> Int -> Int
`unsafeShiftL` (I#i# :: Int#
i# )=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`uncheckedIShiftL#`Int#
i# )(I#x# :: Int#
x# )shiftR :: Int -> Int -> Int
`shiftR` (I#i# :: Int#
i# )|Int# -> Bool
isTrue#(Int#
i# Int# -> Int# -> Int#
>=#0#)=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`iShiftRA#` Int#
i# )|Bool
otherwise =Int
forall a. a
overflowError (I#x# :: Int#
x# )unsafeShiftR :: Int -> Int -> Int
`unsafeShiftR` (I#i# :: Int#
i# )=Int# -> Int
I#(Int#
x# Int# -> Int# -> Int#
`uncheckedIShiftRA#`Int#
i# ){-# INLINErotate #-}-- See Note [Constant folding for rotate](I#x# :: Int#
x# )rotate :: Int -> Int -> Int
`rotate` (I#i# :: Int#
i# )=Int# -> Int
I#((Int#
x# Int# -> Int# -> Int#
`uncheckedIShiftL#`Int#
i'# )Int# -> Int# -> Int#
`orI#`(Int#
x# Int# -> Int# -> Int#
`uncheckedIShiftRL#`(Int#
wsib Int# -> Int# -> Int#
-#Int#
i'# )))where!i'# :: Int#
i'# =Int#
i# Int# -> Int# -> Int#
`andI#`(Int#
wsib Int# -> Int# -> Int#
-#1#)!wsib :: Int#
wsib =WORD_SIZE_IN_BITS#{- work around preprocessor problem (??) -}bitSizeMaybe :: Int -> Maybe Int
bitSizeMaybe i :: Int
i =Int -> Maybe Int
forall a. a -> Maybe a
Just (Int -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize Int
i )bitSize :: Int -> Int
bitSize i :: Int
i =Int -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize Int
i popCount :: Int -> Int
popCount (I#x# :: Int#
x# )=Int# -> Int
I#(Word# -> Int#
word2Int#(Word# -> Word#
popCnt#(Int# -> Word#
int2Word#Int#
x# )))isSigned :: Int -> Bool
isSigned _=Bool
True-- | @since 4.6.0.0instanceFiniteBits IntwherefiniteBitSize :: Int -> Int
finiteBitSize _=WORD_SIZE_IN_BITScountLeadingZeros :: Int -> Int
countLeadingZeros (I#x# :: Int#
x# )=Int# -> Int
I#(Word# -> Int#
word2Int#(Word# -> Word#
clz#(Int# -> Word#
int2Word#Int#
x# )))countTrailingZeros :: Int -> Int
countTrailingZeros (I#x# :: Int#
x# )=Int# -> Int
I#(Word# -> Int#
word2Int#(Word# -> Word#
ctz#(Int# -> Word#
int2Word#Int#
x# )))-- | @since 2.01instanceBits Wordwhere{-# INLINEshift #-}{-# INLINEbit #-}{-# INLINEtestBit #-}(W#x# :: Word#
x# ).&. :: Word -> Word -> Word
.&. (W#y# :: Word#
y# )=Word# -> Word
W#(Word#
x# Word# -> Word# -> Word#
`and#`Word#
y# )(W#x# :: Word#
x# ).|. :: Word -> Word -> Word
.|. (W#y# :: Word#
y# )=Word# -> Word
W#(Word#
x# Word# -> Word# -> Word#
`or#`Word#
y# )(W#x# :: Word#
x# )xor :: Word -> Word -> Word
`xor` (W#y# :: Word#
y# )=Word# -> Word
W#(Word#
x# Word# -> Word# -> Word#
`xor#`Word#
y# )complement :: Word -> Word
complement (W#x# :: Word#
x# )=Word# -> Word
W#(Word#
x# Word# -> Word# -> Word#
`xor#`Word#
mb# )where!(W#mb# :: Word#
mb# )=Word
forall a. Bounded a => a
maxBound (W#x# :: Word#
x# )shift :: Word -> Int -> Word
`shift` (I#i# :: Int#
i# )|Int# -> Bool
isTrue#(Int#
i# Int# -> Int# -> Int#
>=#0#)=Word# -> Word
W#(Word#
x# Word# -> Int# -> Word#
`shiftL#` Int#
i# )|Bool
otherwise =Word# -> Word
W#(Word#
x# Word# -> Int# -> Word#
`shiftRL#` Int# -> Int#
negateInt#Int#
i# )(W#x# :: Word#
x# )shiftL :: Word -> Int -> Word
`shiftL` (I#i# :: Int#
i# )|Int# -> Bool
isTrue#(Int#
i# Int# -> Int# -> Int#
>=#0#)=Word# -> Word
W#(Word#
x# Word# -> Int# -> Word#
`shiftL#` Int#
i# )|Bool
otherwise =Word
forall a. a
overflowError (W#x# :: Word#
x# )unsafeShiftL :: Word -> Int -> Word
`unsafeShiftL` (I#i# :: Int#
i# )=Word# -> Word
W#(Word#
x# Word# -> Int# -> Word#
`uncheckedShiftL#`Int#
i# )(W#x# :: Word#
x# )shiftR :: Word -> Int -> Word
`shiftR` (I#i# :: Int#
i# )|Int# -> Bool
isTrue#(Int#
i# Int# -> Int# -> Int#
>=#0#)=Word# -> Word
W#(Word#
x# Word# -> Int# -> Word#
`shiftRL#` Int#
i# )|Bool
otherwise =Word
forall a. a
overflowError (W#x# :: Word#
x# )unsafeShiftR :: Word -> Int -> Word
`unsafeShiftR` (I#i# :: Int#
i# )=Word# -> Word
W#(Word#
x# Word# -> Int# -> Word#
`uncheckedShiftRL#`Int#
i# )(W#x# :: Word#
x# )rotate :: Word -> Int -> Word
`rotate` (I#i# :: Int#
i# )|Int# -> Bool
isTrue#(Int#
i'# Int# -> Int# -> Int#
==#0#)=Word# -> Word
W#Word#
x# |Bool
otherwise =Word# -> Word
W#((Word#
x# Word# -> Int# -> Word#
`uncheckedShiftL#`Int#
i'# )Word# -> Word# -> Word#
`or#`(Word#
x# Word# -> Int# -> Word#
`uncheckedShiftRL#`(Int#
wsib Int# -> Int# -> Int#
-#Int#
i'# )))where!i'# :: Int#
i'# =Int#
i# Int# -> Int# -> Int#
`andI#`(Int#
wsib Int# -> Int# -> Int#
-#1#)!wsib :: Int#
wsib =WORD_SIZE_IN_BITS#{- work around preprocessor problem (??) -}bitSizeMaybe :: Word -> Maybe Int
bitSizeMaybe i :: Word
i =Int -> Maybe Int
forall a. a -> Maybe a
Just (Word -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize Word
i )bitSize :: Word -> Int
bitSize i :: Word
i =Word -> Int
forall b. FiniteBits b => b -> Int
finiteBitSize Word
i isSigned :: Word -> Bool
isSigned _=Bool
FalsepopCount :: Word -> Int
popCount (W#x# :: Word#
x# )=Int# -> Int
I#(Word# -> Int#
word2Int#(Word# -> Word#
popCnt#Word#
x# ))bit :: Int -> Word
bit =Int -> Word
forall a. (Bits a, Num a) => Int -> a
bitDefault testBit :: Word -> Int -> Bool
testBit =Word -> Int -> Bool
forall a. (Bits a, Num a) => a -> Int -> Bool
testBitDefault -- | @since 4.6.0.0instanceFiniteBits WordwherefiniteBitSize :: Word -> Int
finiteBitSize _=WORD_SIZE_IN_BITScountLeadingZeros :: Word -> Int
countLeadingZeros (W#x# :: Word#
x# )=Int# -> Int
I#(Word# -> Int#
word2Int#(Word# -> Word#
clz#Word#
x# ))countTrailingZeros :: Word -> Int
countTrailingZeros (W#x# :: Word#
x# )=Int# -> Int
I#(Word# -> Int#
word2Int#(Word# -> Word#
ctz#Word#
x# ))-- | @since 2.01instanceBits Integerwhere.&. :: Integer -> Integer -> Integer
(.&.) =Integer -> Integer -> Integer
andInteger.|. :: Integer -> Integer -> Integer
(.|.) =Integer -> Integer -> Integer
orIntegerxor :: Integer -> Integer -> Integer
xor =Integer -> Integer -> Integer
xorIntegercomplement :: Integer -> Integer
complement =Integer -> Integer
complementIntegershift :: Integer -> Int -> Integer
shift x :: Integer
x i :: Int
i @(I#i# :: Int#
i# )|Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>=0=Integer -> Int# -> Integer
shiftLIntegerInteger
x Int#
i# |Bool
otherwise =Integer -> Int# -> Integer
shiftRIntegerInteger
x (Int# -> Int#
negateInt#Int#
i# )testBit :: Integer -> Int -> Bool
testBit x :: Integer
x (I#i :: Int#
i )=Integer -> Int# -> Bool
testBitIntegerInteger
x Int#
i zeroBits :: Integer
zeroBits =0bit :: Int -> Integer
bit (I#i# :: Int#
i# )=Int# -> Integer
bitIntegerInt#
i# popCount :: Integer -> Int
popCount x :: Integer
x =Int# -> Int
I#(Integer -> Int#
popCountIntegerInteger
x )rotate :: Integer -> Int -> Integer
rotate x :: Integer
x i :: Int
i =Integer -> Int -> Integer
forall a. Bits a => a -> Int -> a
shift Integer
x Int
i -- since an Integer never wraps aroundbitSizeMaybe :: Integer -> Maybe Int
bitSizeMaybe _=Maybe Int
forall a. Maybe a
Nothing bitSize :: Integer -> Int
bitSize _=[Char] -> Int
forall a. [Char] -> a
errorWithoutStackTrace "Data.Bits.bitSize(Integer)"isSigned :: Integer -> Bool
isSigned _=Bool
True-- | @since 4.8.0instanceBits Natural where.&. :: Natural -> Natural -> Natural
(.&.) =Natural -> Natural -> Natural
andNatural .|. :: Natural -> Natural -> Natural
(.|.) =Natural -> Natural -> Natural
orNatural xor :: Natural -> Natural -> Natural
xor =Natural -> Natural -> Natural
xorNatural complement :: Natural -> Natural
complement _=[Char] -> Natural
forall a. [Char] -> a
errorWithoutStackTrace "Bits.complement: Natural complement undefined"shift :: Natural -> Int -> Natural
shift x :: Natural
x i :: Int
i |Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>=0=Natural -> Int -> Natural
shiftLNatural Natural
x Int
i |Bool
otherwise =Natural -> Int -> Natural
shiftRNatural Natural
x (Int -> Int
forall a. Num a => a -> a
negate Int
i )testBit :: Natural -> Int -> Bool
testBit x :: Natural
x i :: Int
i =Natural -> Int -> Bool
testBitNatural Natural
x Int
i zeroBits :: Natural
zeroBits =Word# -> Natural
wordToNaturalBase 0##clearBit :: Natural -> Int -> Natural
clearBit x :: Natural
x i :: Int
i =Natural
x Natural -> Natural -> Natural
forall a. Bits a => a -> a -> a
`xor` (Int -> Natural
forall a. Bits a => Int -> a
bit Int
i Natural -> Natural -> Natural
forall a. Bits a => a -> a -> a
.&. Natural
x )bit :: Int -> Natural
bit (I#i# :: Int#
i# )=Int# -> Natural
bitNatural Int#
i# popCount :: Natural -> Int
popCount x :: Natural
x =Natural -> Int
popCountNatural Natural
x rotate :: Natural -> Int -> Natural
rotate x :: Natural
x i :: Int
i =Natural -> Int -> Natural
forall a. Bits a => a -> Int -> a
shift Natural
x Int
i -- since an Natural never wraps aroundbitSizeMaybe :: Natural -> Maybe Int
bitSizeMaybe _=Maybe Int
forall a. Maybe a
Nothing bitSize :: Natural -> Int
bitSize _=[Char] -> Int
forall a. [Char] -> a
errorWithoutStackTrace "Data.Bits.bitSize(Natural)"isSigned :: Natural -> Bool
isSigned _=Bool
False------------------------------------------------------------------------------- | Attempt to convert an 'Integral' type @a@ to an 'Integral' type @b@ using-- the size of the types as measured by 'Bits' methods.---- A simpler version of this function is:---- > toIntegral :: (Integral a, Integral b) => a -> Maybe b-- > toIntegral x-- > | toInteger x == y = Just (fromInteger y)-- > | otherwise = Nothing-- > where-- > y = toInteger x---- This version requires going through 'Integer', which can be inefficient.-- However, @toIntegralSized@ is optimized to allow GHC to statically determine-- the relative type sizes (as measured by 'bitSizeMaybe' and 'isSigned') and-- avoid going through 'Integer' for many types. (The implementation uses-- 'fromIntegral', which is itself optimized with rules for @base@ types but may-- go through 'Integer' for some type pairs.)---- @since 4.8.0.0toIntegralSized ::(Integral a ,Integral b ,Bits a ,Bits b )=>a ->Maybe b toIntegralSized :: a -> Maybe b
toIntegralSized x :: a
x -- See Note [toIntegralSized optimization]|Bool -> (a -> Bool) -> Maybe a -> Bool
forall b a. b -> (a -> b) -> Maybe a -> b
maybe Bool
True(a -> a -> Bool
forall a. Ord a => a -> a -> Bool
<=a
x )Maybe a
yMinBound ,Bool -> (a -> Bool) -> Maybe a -> Bool
forall b a. b -> (a -> b) -> Maybe a -> b
maybe Bool
True(a
x a -> a -> Bool
forall a. Ord a => a -> a -> Bool
<=)Maybe a
yMaxBound =b -> Maybe b
forall a. a -> Maybe a
Just b
y |Bool
otherwise =Maybe b
forall a. Maybe a
Nothing wherey :: b
y =a -> b
forall a b. (Integral a, Num b) => a -> b
fromIntegral a
x xWidth :: Maybe Int
xWidth =a -> Maybe Int
forall a. Bits a => a -> Maybe Int
bitSizeMaybe a
x yWidth :: Maybe Int
yWidth =b -> Maybe Int
forall a. Bits a => a -> Maybe Int
bitSizeMaybe b
y yMinBound :: Maybe a
yMinBound |a -> b -> Bool
forall a b. (Bits a, Bits b) => a -> b -> Bool
isBitSubType a
x b
y =Maybe a
forall a. Maybe a
Nothing |a -> Bool
forall a. Bits a => a -> Bool
isSigned a
x ,Bool -> Bool
not(b -> Bool
forall a. Bits a => a -> Bool
isSigned b
y )=a -> Maybe a
forall a. a -> Maybe a
Just 0|a -> Bool
forall a. Bits a => a -> Bool
isSigned a
x ,b -> Bool
forall a. Bits a => a -> Bool
isSigned b
y ,Just yW :: Int
yW <-Maybe Int
yWidth =a -> Maybe a
forall a. a -> Maybe a
Just (a -> a
forall a. Num a => a -> a
negate (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$ Int -> a
forall a. Bits a => Int -> a
bit (Int
yW Int -> Int -> Int
forall a. Num a => a -> a -> a
- 1))-- Assumes sub-type|Bool
otherwise =Maybe a
forall a. Maybe a
Nothing yMaxBound :: Maybe a
yMaxBound |a -> b -> Bool
forall a b. (Bits a, Bits b) => a -> b -> Bool
isBitSubType a
x b
y =Maybe a
forall a. Maybe a
Nothing |a -> Bool
forall a. Bits a => a -> Bool
isSigned a
x ,Bool -> Bool
not(b -> Bool
forall a. Bits a => a -> Bool
isSigned b
y ),Just xW :: Int
xW <-Maybe Int
xWidth ,Just yW :: Int
yW <-Maybe Int
yWidth ,Int
xW Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<=Int
yW Int -> Int -> Int
forall a. Num a => a -> a -> a
+ 1=Maybe a
forall a. Maybe a
Nothing -- Max bound beyond a's domain|Just yW :: Int
yW <-Maybe Int
yWidth =ifb -> Bool
forall a. Bits a => a -> Bool
isSigned b
y thena -> Maybe a
forall a. a -> Maybe a
Just (Int -> a
forall a. Bits a => Int -> a
bit (Int
yW Int -> Int -> Int
forall a. Num a => a -> a -> a
- 1)a -> a -> a
forall a. Num a => a -> a -> a
- 1)elsea -> Maybe a
forall a. a -> Maybe a
Just (Int -> a
forall a. Bits a => Int -> a
bit Int
yW a -> a -> a
forall a. Num a => a -> a -> a
- 1)|Bool
otherwise =Maybe a
forall a. Maybe a
Nothing {-# INLINABLEtoIntegralSized #-}-- | 'True' if the size of @a@ is @<=@ the size of @b@, where size is measured-- by 'bitSizeMaybe' and 'isSigned'.isBitSubType ::(Bits a ,Bits b )=>a ->b ->BoolisBitSubType :: a -> b -> Bool
isBitSubType x :: a
x y :: b
y -- Reflexive|Maybe Int
xWidth Maybe Int -> Maybe Int -> Bool
forall a. Eq a => a -> a -> Bool
==Maybe Int
yWidth ,Bool
xSigned Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
==Bool
ySigned =Bool
True-- Every integer is a subset of 'Integer'|Bool
ySigned ,Maybe Int
forall a. Maybe a
Nothing Maybe Int -> Maybe Int -> Bool
forall a. Eq a => a -> a -> Bool
==Maybe Int
yWidth =Bool
True|Bool -> Bool
notBool
xSigned ,Bool -> Bool
notBool
ySigned ,Maybe Int
forall a. Maybe a
Nothing Maybe Int -> Maybe Int -> Bool
forall a. Eq a => a -> a -> Bool
==Maybe Int
yWidth =Bool
True-- Sub-type relations between fixed-with types|Bool
xSigned Bool -> Bool -> Bool
forall a. Eq a => a -> a -> Bool
==Bool
ySigned ,Just xW :: Int
xW <-Maybe Int
xWidth ,Just yW :: Int
yW <-Maybe Int
yWidth =Int
xW Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<=Int
yW |Bool -> Bool
notBool
xSigned ,Bool
ySigned ,Just xW :: Int
xW <-Maybe Int
xWidth ,Just yW :: Int
yW <-Maybe Int
yWidth =Int
xW Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
yW |Bool
otherwise =Bool
FalsewherexWidth :: Maybe Int
xWidth =a -> Maybe Int
forall a. Bits a => a -> Maybe Int
bitSizeMaybe a
x xSigned :: Bool
xSigned =a -> Bool
forall a. Bits a => a -> Bool
isSigned a
x yWidth :: Maybe Int
yWidth =b -> Maybe Int
forall a. Bits a => a -> Maybe Int
bitSizeMaybe b
y ySigned :: Bool
ySigned =b -> Bool
forall a. Bits a => a -> Bool
isSigned b
y {-# INLINEisBitSubType #-}{- 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
 }
-}-- Note [toIntegralSized optimization]-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-- The code in 'toIntegralSized' relies on GHC optimizing away statically-- decidable branches.---- If both integral types are statically known, GHC will be able optimize the-- code significantly (for @-O1@ and better).---- For instance (as of GHC 7.8.1) the following definitions:---- > w16_to_i32 = toIntegralSized :: Word16 -> Maybe Int32-- >-- > i16_to_w16 = toIntegralSized :: Int16 -> Maybe Word16---- are translated into the following (simplified) /GHC Core/ language:---- > w16_to_i32 = \x -> Just (case x of _ { W16# x# -> I32# (word2Int# x#) })-- >-- > i16_to_w16 = \x -> case eta of _-- > { I16# b1 -> case tagToEnum# (<=# 0 b1) of _-- > { False -> Nothing-- > ; True -> Just (W16# (narrow16Word# (int2Word# b1)))-- > }-- > }