{-# 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 #if defined(MIN_VERSION_integer_gmp)
importGHC.Integer.GMP.Internals(bitInteger,popCountInteger)#endif
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 `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 4.7.0.0zeroBits ::a zeroBits =clearBit (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 =fromMaybe (error "bitSize is undefined")(bitSizeMaybe 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 `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 {-# INLINEshiftL#-}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 {-# INLINEunsafeShiftL#-}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 {-# INLINEshiftR#-}x `shiftR `i =x `shift `(-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 `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 {-# INLINErotateL#-}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 {-# INLINErotateR#-}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.
 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 =(w -1)-go (w -1)wherego i |i <0=i -- no bit set|testBit x i =i |otherwise =go (i -1)w =finiteBitSize 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 =go 0wherego i |i >=w =i |testBit x i =i |otherwise =go (i + 1)w =finiteBitSize 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 =\i ->1`shiftL `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 =\x i ->(x .&. bit i )/=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 =go 0wherego !c 0=c goc w =go (c + 1)(w .&. (w -1))-- clear the least significant{-# INLINABLEpopCountDefault#-}-- | Interpret 'Bool' as 1-bit bit-field---- @since 4.7.0.0instanceBits Boolwhere(.&. )=(&&)(.|. )=(||)xor =(/=)complement =notshift x 0=x shift__=Falserotate x _=x bit 0=Truebit_=FalsetestBit x 0=x testBit__=FalsebitSizeMaybe _=Just 1bitSize _=1isSigned _=FalsepopCount False=0popCountTrue=1-- | @since 4.7.0.0instanceFiniteBits BoolwherefiniteBitSize _=1countTrailingZeros x =ifx then0else1countLeadingZeros x =ifx then0else1-- | @since 2.01instanceBits Intwhere{-# INLINEshift#-}{-# INLINEbit#-}{-# INLINEtestBit#-}zeroBits =0bit =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# ){-# INLINErotate#-}-- 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-- | @since 4.6.0.0instanceFiniteBits IntwherefiniteBitSize _=WORD_SIZE_IN_BITScountLeadingZeros (I#x# )=I#(word2Int#(clz#(int2Word#x# )))countTrailingZeros (I#x# )=I#(word2Int#(ctz#(int2Word#x# )))-- | @since 2.01instanceBits Wordwhere{-# INLINEshift#-}{-# INLINEbit#-}{-# INLINEtestBit#-}(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 _=FalsepopCount (W#x# )=I#(word2Int#(popCnt#x# ))bit =bitDefault testBit =testBitDefault -- | @since 4.6.0.0instanceFiniteBits WordwherefiniteBitSize _=WORD_SIZE_IN_BITScountLeadingZeros (W#x# )=I#(word2Int#(clz#x# ))countTrailingZeros (W#x# )=I#(word2Int#(ctz#x# ))-- | @since 2.01instanceBits Integerwhere(.&. )=andInteger(.|. )=orIntegerxor =xorIntegercomplement =complementIntegershift x i @(I#i# )|i >=0=shiftLIntegerx i# |otherwise =shiftRIntegerx (negateInt#i# )testBit x (I#i )=testBitIntegerx i zeroBits =0#if defined(MIN_VERSION_integer_gmp)
bit (I#i# )=bitIntegeri# popCount x =I#(popCountIntegerx )#else
bit=bitDefaultpopCount=popCountDefault#endif
rotate x i =shift x i -- since an Integer never wraps aroundbitSizeMaybe _=Nothing bitSize _=errorWithoutStackTrace "Data.Bits.bitSize(Integer)"isSigned _=True#if defined(MIN_VERSION_integer_gmp)
-- | @since 4.8.0instanceBits Natural where(.&. )=andNatural (.|. )=orNatural xor =xorNatural complement _=errorWithoutStackTrace "Bits.complement: Natural complement undefined"shift x i |i >=0=shiftLNatural x i |otherwise =shiftRNatural x (negate i )testBit x i =testBitNatural x i zeroBits =wordToNaturalBase 0##clearBit x i =x `xor `(bit i .&. x )bit (I#i# )=bitNatural i# popCount x =popCountNatural x rotate x i =shift x i -- since an Natural never wraps aroundbitSizeMaybe _=Nothing bitSize _=errorWithoutStackTrace "Data.Bits.bitSize(Natural)"isSigned _=False#else
-- | @since 4.8.0.0instanceBitsNaturalwhereNaturaln.&.Naturalm=Natural(n.&.m){-# INLINE(.&.)#-}Naturaln.|.Naturalm=Natural(n.|.m){-# INLINE(.|.)#-}xor(Naturaln)(Naturalm)=Natural(xornm){-# INLINExor#-}complement_=errorWithoutStackTrace"Bits.complement: Natural complement undefined"{-# INLINEcomplement#-}shift(Naturaln)=Natural.shiftn{-# INLINEshift#-}rotate(Naturaln)=Natural.rotaten{-# INLINErotate#-}bit=Natural.bit{-# INLINEbit#-}setBit(Naturaln)=Natural.setBitn{-# INLINEsetBit#-}clearBit(Naturaln)=Natural.clearBitn{-# INLINEclearBit#-}complementBit(Naturaln)=Natural.complementBitn{-# INLINEcomplementBit#-}testBit(Naturaln)=testBitn{-# INLINEtestBit#-}bitSizeMaybe_=Nothing{-# INLINEbitSizeMaybe#-}bitSize=errorWithoutStackTrace"Natural: bitSize"{-# INLINEbitSize#-}isSigned_=False{-# INLINEisSigned#-}shiftL(Naturaln)=Natural.shiftLn{-# INLINEshiftL#-}shiftR(Naturaln)=Natural.shiftRn{-# INLINEshiftR#-}rotateL(Naturaln)=Natural.rotateLn{-# INLINErotateL#-}rotateR(Naturaln)=Natural.rotateRn{-# INLINErotateR#-}popCount(Naturaln)=popCountn{-# INLINEpopCount#-}zeroBits=Natural0#endif
------------------------------------------------------------------------------- | 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 x -- See Note [toIntegralSized optimization]|maybe True(<=x )yMinBound ,maybe True(x <=)yMaxBound =Just y |otherwise =Nothing wherey =fromIntegral x xWidth =bitSizeMaybe x yWidth =bitSizeMaybe y yMinBound |isBitSubType x y =Nothing |isSigned x ,not(isSigned y )=Just 0|isSigned x ,isSigned y ,Just yW <-yWidth =Just (negate $ bit (yW -1))-- Assumes sub-type|otherwise =Nothing yMaxBound |isBitSubType x y =Nothing |isSigned x ,not(isSigned y ),Just xW <-xWidth ,Just yW <-yWidth ,xW <=yW + 1=Nothing -- Max bound beyond a's domain|Just yW <-yWidth =ifisSigned y thenJust (bit (yW -1)-1)elseJust (bit yW -1)|otherwise =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 x y -- Reflexive|xWidth ==yWidth ,xSigned ==ySigned =True-- Every integer is a subset of 'Integer'|ySigned ,Nothing ==yWidth =True|notxSigned ,notySigned ,Nothing ==yWidth =True-- Sub-type relations between fixed-with types|xSigned ==ySigned ,Just xW <-xWidth ,Just yW <-yWidth =xW <=yW |notxSigned ,ySigned ,Just xW <-xWidth ,Just yW <-yWidth =xW <yW |otherwise =FalsewherexWidth =bitSizeMaybe x xSigned =isSigned x yWidth =bitSizeMaybe y ySigned =isSigned 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)))-- > }-- > }