Data.Bits
| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | stable |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Contents
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.
Type classes
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.
Minimal complete definition
(.&.), (.|.), xor, complement, (shift | shiftL, shiftR), (rotate | rotateL, rotateR), bitSize, bitSizeMaybe, isSigned, testBit, bit, popCount
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 is the value with all bits unset.
The following laws ought to hold (for all valid bit indices n):
clearBit zeroBits n == zeroBitssetBit zeroBits n == bit ntestBit zeroBits n == FalsepopCount 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: base-4.7.0.0
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
x `testBit` i is the same as x .&. bit n /= 0
In other words it returns True if the bit at offset @n is set.
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
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.
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.
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
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
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
Extra functions
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 == toInteger y = Just y
| otherwise = Nothing
where
y = fromIntegral xThis 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
oneBits :: FiniteBits a => a Source
A more concise version of complement zeroBits.
>>> complement (zeroBits :: Word) == (oneBits :: Word)
True
>>> complement (oneBits :: Word) == (zeroBits :: Word)
True
Note
The constraint on oneBits is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.
Since: base-4.16
(.^.) :: Bits a => a -> a -> a infixl 6 Source
Infix version of xor.
Since: base-4.17
(.>>.) :: Bits a => a -> Int -> a infixl 8 Source
Infix version of shiftR.
Since: base-4.17
(.<<.) :: Bits a => a -> Int -> a infixl 8 Source
Infix version of shiftL.
Since: base-4.17
(!>>.) :: Bits a => a -> Int -> a infixl 8 Source
Infix version of unsafeShiftR.
Since: base-4.17
(!<<.) :: Bits a => a -> Int -> a infixl 8 Source
Infix version of unsafeShiftL.
Since: base-4.17
Newtypes
Monoid under bitwise AND.
>>> getAnd (And 0xab <> And 0x12) :: Word8
2
Since: base-4.16
Instances
| FiniteBits a => Monoid (And a) Source | This constraint is arguably too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Semigroup (And a) Source | Since: base-4.16 |
| Bits a => Bits (And a) Source | Since: base-4.16 |
|
Defined in Data.Bits Methods(.&.) :: And a -> And a -> And a Source (.|.) :: And a -> And a -> And a Source xor :: And a -> And a -> And a Source complement :: And a -> And a Source shift :: And a -> Int -> And a Source rotate :: And a -> Int -> And a Source setBit :: And a -> Int -> And a Source clearBit :: And a -> Int -> And a Source complementBit :: And a -> Int -> And a Source testBit :: And a -> Int -> Bool Source bitSizeMaybe :: And a -> Maybe Int Source bitSize :: And a -> Int Source isSigned :: And a -> Bool Source shiftL :: And a -> Int -> And a Source unsafeShiftL :: And a -> Int -> And a Source shiftR :: And a -> Int -> And a Source unsafeShiftR :: And a -> Int -> And a Source rotateL :: And a -> Int -> And a Source |
|
| FiniteBits a => FiniteBits (And a) Source | Since: base-4.16 |
|
Defined in Data.Bits MethodsfiniteBitSize :: And a -> Int Source countLeadingZeros :: And a -> Int Source countTrailingZeros :: And a -> Int Source |
|
| Bounded a => Bounded (And a) Source | Since: base-4.16 |
| Enum a => Enum (And a) Source | Since: base-4.16 |
| Read a => Read (And a) Source | Since: base-4.16 |
| Show a => Show (And a) Source | Since: base-4.16 |
| Eq a => Eq (And a) Source | Since: base-4.16 |
Monoid under bitwise inclusive OR.
>>> getIor (Ior 0xab <> Ior 0x12) :: Word8
187
Since: base-4.16
Instances
Monoid under bitwise XOR.
>>> getXor (Xor 0xab <> Xor 0x12) :: Word8
185
Since: base-4.16
Instances
Monoid under bitwise 'equality'; defined as 1 if the corresponding bits match, and 0 otherwise.
>>> getIff (Iff 0xab <> Iff 0x12) :: Word8
70
Since: base-4.16
Instances
| FiniteBits a => Monoid (Iff a) Source | This constraint is arguably too strong. However, as some types (such as Since: base-4.16 |
| FiniteBits a => Semigroup (Iff a) Source | This constraint is arguably too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Bits (Iff a) Source | Since: base-4.16 |
|
Defined in Data.Bits Methods(.&.) :: Iff a -> Iff a -> Iff a Source (.|.) :: Iff a -> Iff a -> Iff a Source xor :: Iff a -> Iff a -> Iff a Source complement :: Iff a -> Iff a Source shift :: Iff a -> Int -> Iff a Source rotate :: Iff a -> Int -> Iff a Source setBit :: Iff a -> Int -> Iff a Source clearBit :: Iff a -> Int -> Iff a Source complementBit :: Iff a -> Int -> Iff a Source testBit :: Iff a -> Int -> Bool Source bitSizeMaybe :: Iff a -> Maybe Int Source bitSize :: Iff a -> Int Source isSigned :: Iff a -> Bool Source shiftL :: Iff a -> Int -> Iff a Source unsafeShiftL :: Iff a -> Int -> Iff a Source shiftR :: Iff a -> Int -> Iff a Source unsafeShiftR :: Iff a -> Int -> Iff a Source rotateL :: Iff a -> Int -> Iff a Source |
|
| FiniteBits a => FiniteBits (Iff a) Source | Since: base-4.16 |
|
Defined in Data.Bits MethodsfiniteBitSize :: Iff a -> Int Source countLeadingZeros :: Iff a -> Int Source countTrailingZeros :: Iff a -> Int Source |
|
| Bounded a => Bounded (Iff a) Source | Since: base-4.16 |
| Enum a => Enum (Iff a) Source | Since: base-4.16 |
| Read a => Read (Iff a) Source | Since: base-4.16 |
| Show a => Show (Iff a) Source | Since: base-4.16 |
| Eq a => Eq (Iff a) Source | Since: base-4.16 |
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/Data-Bits.html