W3cubDocs

/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: 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: 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.

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).

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: 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.

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 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

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: 4.5.0.0

Instances

Bits Bool

Interpret Bool as 1-bit bit-field

Since: 4.7.0.0

Bits Int

Since: 2.1

Bits Int8

Since: 2.1

Bits Int16

Since: 2.1

Bits Int32

Since: 2.1

Bits Int64

Since: 2.1

Bits Integer

Since: 2.1

Bits Natural

Since: 4.8.0.0

Bits Word

Since: 2.1

Bits Word8

Since: 2.1

Bits Word16

Since: 2.1

Bits Word32

Since: 2.1

Bits Word64

Since: 2.1

Bits IntPtr
Bits WordPtr
Bits CUIntMax
Bits CIntMax
Bits CUIntPtr
Bits CIntPtr
Bits CSigAtomic
Bits CWchar
Bits CSize
Bits CPtrdiff
Bits CBool
Bits CULLong
Bits CLLong
Bits CULong
Bits CLong
Bits CUInt
Bits CInt
Bits CUShort
Bits CShort
Bits CUChar
Bits CSChar
Bits CChar
Bits Fd
Bits CKey
Bits CId
Bits CFsFilCnt
Bits CFsBlkCnt
Bits CClockId
Bits CBlkCnt
Bits CBlkSize
Bits CRLim
Bits CTcflag
Bits CUid
Bits CNlink
Bits CGid
Bits CSsize
Bits CPid
Bits COff
Bits CMode
Bits CIno
Bits CDev
Bits a => Bits (Identity a)
Bits a => Bits (Const k a b)

Methods

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

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

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

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

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

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

zeroBits :: Const k a b Source

bit :: Int -> Const k a b Source

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

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

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

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

bitSizeMaybe :: Const k a b -> Maybe Int Source

bitSize :: Const k a b -> Int Source

isSigned :: Const k a b -> Bool Source

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

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

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

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

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

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

popCount :: Const k a b -> Int Source

class Bits b => FiniteBits b where Source

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

Since: 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: 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: 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: 4.8.0.0

Instances

FiniteBits Bool

Since: 4.7.0.0

FiniteBits Int

Since: 4.6.0.0

FiniteBits Int8

Since: 4.6.0.0

FiniteBits Int16

Since: 4.6.0.0

FiniteBits Int32

Since: 4.6.0.0

FiniteBits Int64

Since: 4.6.0.0

FiniteBits Word

Since: 4.6.0.0

FiniteBits Word8

Since: 4.6.0.0

FiniteBits Word16

Since: 4.6.0.0

FiniteBits Word32

Since: 4.6.0.0

FiniteBits Word64

Since: 4.6.0.0

FiniteBits IntPtr
FiniteBits WordPtr
FiniteBits CUIntMax
FiniteBits CIntMax
FiniteBits CUIntPtr
FiniteBits CIntPtr
FiniteBits CSigAtomic
FiniteBits CWchar
FiniteBits CSize
FiniteBits CPtrdiff
FiniteBits CBool
FiniteBits CULLong
FiniteBits CLLong
FiniteBits CULong
FiniteBits CLong
FiniteBits CUInt
FiniteBits CInt
FiniteBits CUShort
FiniteBits CShort
FiniteBits CUChar
FiniteBits CSChar
FiniteBits CChar
FiniteBits Fd
FiniteBits CKey
FiniteBits CId
FiniteBits CFsFilCnt
FiniteBits CFsBlkCnt
FiniteBits CClockId
FiniteBits CBlkCnt
FiniteBits CBlkSize
FiniteBits CRLim
FiniteBits CTcflag
FiniteBits CUid
FiniteBits CNlink
FiniteBits CGid
FiniteBits CSsize
FiniteBits CPid
FiniteBits COff
FiniteBits CMode
FiniteBits CIno
FiniteBits CDev
FiniteBits a => FiniteBits (Identity a)
FiniteBits a => FiniteBits (Const k a b)

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

Default implementation for bit.

Note that: bitDefault i = 1 shiftL i

Since: 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: 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: 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: 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/8.2.1/docs/html/libraries/base-4.10.0.0/Data-Bits.html