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/Haskell 8

Data.Bits

Copyright (c) The University of Glasgow 2001
License BSD-style (see the file libraries/base/LICENSE)
Maintainer [email protected]
Stability experimental
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

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.

class Eq a => Bits a where Source

The Bits class defines bitwise operations over integral types.

  • Bits are numbered from 0 with bit 0 being the least significant bit.

Methods

(.&.) :: a -> a -> a infixl 7 Source

Bitwise "and"

(.|.) :: a -> a -> a infixl 5 Source

Bitwise "or"

xor :: a -> a -> a infixl 6 Source

Bitwise "xor"

complement :: a -> a Source

Reverse all the bits in the argument

shift :: a -> Int -> a infixl 8 Source

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.

rotate :: a -> Int -> a infixl 8 Source

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.

zeroBits :: a Source

zeroBits is the value with all bits unset.

The following laws ought to hold (for all valid bit indices n):

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: base-4.7.0.0

bit :: Int -> a Source

bit i is a value with the ith bit set and all other bits clear.

Can be implemented using bitDefault if a is also an instance of Num.

See also zeroBits.

setBit :: a -> Int -> a Source

x `setBit` i is the same as x .|. bit i

clearBit :: a -> Int -> a Source

x `clearBit` i is the same as x .&. complement (bit i)

complementBit :: a -> Int -> a Source

x `complementBit` i is the same as x `xor` bit i

testBit :: a -> Int -> Bool Source

Return True if the nth bit of the argument is 1

Can be implemented using testBitDefault if a is also an instance of Num.

bitSizeMaybe :: a -> Maybe Int Source

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: base-4.7.0.0

bitSize :: a -> Int Source

Deprecated: Use bitSizeMaybe or finiteBitSize instead

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.

isSigned :: a -> Bool Source

Return True if the argument is a signed type. The actual value of the argument is ignored

shiftL :: a -> Int -> a infixl 8 Source

Shift the argument left by the specified number of bits (which must be non-negative). Some instances may throw an 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.

unsafeShiftL :: a -> Int -> a Source

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: base-4.5.0.0

shiftR :: a -> Int -> a infixl 8 Source

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 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.

unsafeShiftR :: a -> Int -> a Source

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: base-4.5.0.0

rotateL :: a -> Int -> a infixl 8 Source

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.

rotateR :: a -> Int -> a infixl 8 Source

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.

popCount :: a -> Int Source

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: base-4.5.0.0

Instances
Instances details
Bits Bool

Interpret Bool as 1-bit bit-field

Since: base-4.7.0.0

Instance details

Defined in Data.Bits

Bits Int

Since: base-2.1

Instance details

Defined in Data.Bits

Bits Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Integer

Since: base-2.1

Instance details

Defined in Data.Bits

Bits Natural

Since: base-4.8.0

Instance details

Defined in Data.Bits

Bits Word

Since: base-2.1

Instance details

Defined in Data.Bits

Bits Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Bits Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Bits Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Bits Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Bits IntPtr
Instance details

Defined in Foreign.Ptr

Bits WordPtr
Instance details

Defined in Foreign.Ptr

Bits CUIntMax
Instance details

Defined in Foreign.C.Types

Bits CIntMax
Instance details

Defined in Foreign.C.Types

Bits CUIntPtr
Instance details

Defined in Foreign.C.Types

Bits CIntPtr
Instance details

Defined in Foreign.C.Types

Bits CSigAtomic
Instance details

Defined in Foreign.C.Types

Bits CWchar
Instance details

Defined in Foreign.C.Types

Bits CSize
Instance details

Defined in Foreign.C.Types

Bits CPtrdiff
Instance details

Defined in Foreign.C.Types

Bits CBool
Instance details

Defined in Foreign.C.Types

Bits CULLong
Instance details

Defined in Foreign.C.Types

Bits CLLong
Instance details

Defined in Foreign.C.Types

Bits CULong
Instance details

Defined in Foreign.C.Types

Bits CLong
Instance details

Defined in Foreign.C.Types

Bits CUInt
Instance details

Defined in Foreign.C.Types

Bits CInt
Instance details

Defined in Foreign.C.Types

Bits CUShort
Instance details

Defined in Foreign.C.Types

Bits CShort
Instance details

Defined in Foreign.C.Types

Bits CUChar
Instance details

Defined in Foreign.C.Types

Bits CSChar
Instance details

Defined in Foreign.C.Types

Bits CChar
Instance details

Defined in Foreign.C.Types

Bits Fd
Instance details

Defined in System.Posix.Types

Bits CKey
Instance details

Defined in System.Posix.Types

Bits CId
Instance details

Defined in System.Posix.Types

Bits CFsFilCnt
Instance details

Defined in System.Posix.Types

Bits CFsBlkCnt
Instance details

Defined in System.Posix.Types

Bits CClockId
Instance details

Defined in System.Posix.Types

Bits CBlkCnt
Instance details

Defined in System.Posix.Types

Bits CBlkSize
Instance details

Defined in System.Posix.Types

Bits CRLim
Instance details

Defined in System.Posix.Types

Bits CTcflag
Instance details

Defined in System.Posix.Types

Bits CUid
Instance details

Defined in System.Posix.Types

Bits CNlink
Instance details

Defined in System.Posix.Types

Bits CGid
Instance details

Defined in System.Posix.Types

Bits CSsize
Instance details

Defined in System.Posix.Types

Bits CPid
Instance details

Defined in System.Posix.Types

Bits COff
Instance details

Defined in System.Posix.Types

Bits CMode
Instance details

Defined in System.Posix.Types

Bits CIno
Instance details

Defined in System.Posix.Types

Bits CDev
Instance details

Defined in System.Posix.Types

Bits a => Bits (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Bits a => Bits (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(.&.) :: Const a b -> Const a b -> Const a b Source

(.|.) :: Const a b -> Const a b -> Const a b Source

xor :: Const a b -> Const a b -> Const a b Source

complement :: Const a b -> Const a b Source

shift :: Const a b -> Int -> Const a b Source

rotate :: Const a b -> Int -> Const a b Source

zeroBits :: Const a b Source

bit :: Int -> Const a b Source

setBit :: Const a b -> Int -> Const a b Source

clearBit :: Const a b -> Int -> Const a b Source

complementBit :: Const a b -> Int -> Const a b Source

testBit :: Const a b -> Int -> Bool Source

bitSizeMaybe :: Const a b -> Maybe Int Source

bitSize :: Const a b -> Int Source

isSigned :: Const a b -> Bool Source

shiftL :: Const a b -> Int -> Const a b Source

unsafeShiftL :: Const a b -> Int -> Const a b Source

shiftR :: Const a b -> Int -> Const a b Source

unsafeShiftR :: Const a b -> Int -> Const a b Source

rotateL :: Const a b -> Int -> Const a b Source

rotateR :: Const a b -> Int -> Const a b Source

popCount :: Const a b -> Int Source

class Bits b => FiniteBits b where Source

The FiniteBits class denotes types with a finite, fixed number of bits.

Since: base-4.7.0.0

Minimal complete definition

finiteBitSize

Methods

finiteBitSize :: b -> Int Source

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: base-4.7.0.0

countLeadingZeros :: b -> Int Source

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: base-4.8.0.0

countTrailingZeros :: b -> Int Source

Count number of zero bits following the least significant set bit.

countTrailingZeros (zeroBits :: a) = finiteBitSize (zeroBits :: a)
countTrailingZeros . negate = countTrailingZeros

The related 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: base-4.8.0.0

Instances
Instances details
FiniteBits Bool

Since: base-4.7.0.0

Instance details

Defined in Data.Bits

FiniteBits Int

Since: base-4.6.0.0

Instance details

Defined in Data.Bits

FiniteBits Int8

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Int16

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Int32

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Int64

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Word

Since: base-4.6.0.0

Instance details

Defined in Data.Bits

FiniteBits Word8

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits Word16

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits Word32

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits Word64

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits IntPtr
Instance details

Defined in Foreign.Ptr

FiniteBits WordPtr
Instance details

Defined in Foreign.Ptr

FiniteBits CUIntMax
Instance details

Defined in Foreign.C.Types

FiniteBits CIntMax
Instance details

Defined in Foreign.C.Types

FiniteBits CUIntPtr
Instance details

Defined in Foreign.C.Types

FiniteBits CIntPtr
Instance details

Defined in Foreign.C.Types

FiniteBits CSigAtomic
Instance details

Defined in Foreign.C.Types

FiniteBits CWchar
Instance details

Defined in Foreign.C.Types

FiniteBits CSize
Instance details

Defined in Foreign.C.Types

FiniteBits CPtrdiff
Instance details

Defined in Foreign.C.Types

FiniteBits CBool
Instance details

Defined in Foreign.C.Types

FiniteBits CULLong
Instance details

Defined in Foreign.C.Types

FiniteBits CLLong
Instance details

Defined in Foreign.C.Types

FiniteBits CULong
Instance details

Defined in Foreign.C.Types

FiniteBits CLong
Instance details

Defined in Foreign.C.Types

FiniteBits CUInt
Instance details

Defined in Foreign.C.Types

FiniteBits CInt
Instance details

Defined in Foreign.C.Types

FiniteBits CUShort
Instance details

Defined in Foreign.C.Types

FiniteBits CShort
Instance details

Defined in Foreign.C.Types

FiniteBits CUChar
Instance details

Defined in Foreign.C.Types

FiniteBits CSChar
Instance details

Defined in Foreign.C.Types

FiniteBits CChar
Instance details

Defined in Foreign.C.Types

FiniteBits Fd
Instance details

Defined in System.Posix.Types

FiniteBits CKey
Instance details

Defined in System.Posix.Types

FiniteBits CId
Instance details

Defined in System.Posix.Types

FiniteBits CFsFilCnt
Instance details

Defined in System.Posix.Types

FiniteBits CFsBlkCnt
Instance details

Defined in System.Posix.Types

FiniteBits CClockId
Instance details

Defined in System.Posix.Types

FiniteBits CBlkCnt
Instance details

Defined in System.Posix.Types

FiniteBits CBlkSize
Instance details

Defined in System.Posix.Types

FiniteBits CRLim
Instance details

Defined in System.Posix.Types

FiniteBits CTcflag
Instance details

Defined in System.Posix.Types

FiniteBits CUid
Instance details

Defined in System.Posix.Types

FiniteBits CNlink
Instance details

Defined in System.Posix.Types

FiniteBits CGid
Instance details

Defined in System.Posix.Types

FiniteBits CSsize
Instance details

Defined in System.Posix.Types

FiniteBits CPid
Instance details

Defined in System.Posix.Types

FiniteBits COff
Instance details

Defined in System.Posix.Types

FiniteBits CMode
Instance details

Defined in System.Posix.Types

FiniteBits CIno
Instance details

Defined in System.Posix.Types

FiniteBits CDev
Instance details

Defined in System.Posix.Types

FiniteBits a => FiniteBits (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

FiniteBits a => FiniteBits (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

bitDefault :: (Bits a, Num a) => Int -> a Source

Default implementation for bit.

Note that: bitDefault i = 1 shiftL i

Since: base-4.6.0.0

testBitDefault :: (Bits a, Num a) => a -> Int -> Bool Source

Default implementation for testBit.

Note that: testBitDefault x i = (x .&. bit i) /= 0

Since: base-4.6.0.0

popCountDefault :: (Bits a, Num a) => a -> Int Source

Default implementation for popCount.

This implementation is intentionally naive. Instances are expected to provide an optimized implementation for their size.

Since: base-4.6.0.0

toIntegralSized :: (Integral a, Integral b, Bits a, Bits b) => a -> Maybe b Source

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: base-4.8.0.0

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/base-4.13.0.0/Data-Bits.html