| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Data.Bits
Description
Synopsis
- class Eq a => Bits a where
- (.&.) :: a -> a -> a
- (.|.) :: a -> a -> a
- xor :: a -> a -> a
- complement :: a -> a
- shift :: a -> Int -> a
- rotate :: a -> Int -> a
- zeroBits :: a
- bit :: Int -> a
- setBit :: a -> Int -> a
- clearBit :: a -> Int -> a
- complementBit :: a -> Int -> a
- testBit :: a -> Int -> Bool
- bitSizeMaybe :: a -> Maybe Int
- bitSize :: a -> Int
- isSigned :: a -> Bool
- shiftL :: a -> Int -> a
- unsafeShiftL :: a -> Int -> a
- shiftR :: a -> Int -> a
- unsafeShiftR :: a -> Int -> a
- rotateL :: a -> Int -> a
- rotateR :: a -> Int -> a
- popCount :: a -> Int
- class Bits b => FiniteBits b where
- finiteBitSize :: b -> Int
- countLeadingZeros :: b -> Int
- countTrailingZeros :: b -> Int
- bitDefault :: (Bits a, Num a) => Int -> a
- testBitDefault :: (Bits a, Num a) => a -> Int -> Bool
- popCountDefault :: (Bits a, Num a) => a -> Int
- toIntegralSized :: (Integral a, Integral b, Bits a, Bits b) => a -> Maybe b
Documentation
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 #
Bitwise "and"
(.|.) :: a -> a -> a infixl 5 #
Bitwise "or"
Bitwise "xor"
complement :: a -> a #
Reverse all the bits in the argument
shift :: a -> Int -> a infixl 8 #
shift x ix 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 #
rotate x ix 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):
clearBitzeroBitsn ==zeroBitssetBitzeroBitsn ==bitntestBitzeroBitsn == FalsepopCountzeroBits== 0
This method uses clearBit (bit 0) 0zeroBits 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.
x `setBit` i is the same as x .|. bit i
x `clearBit` i is the same as x .&. complement (bit i)
complementBit :: a -> Int -> a #
x `complementBit` i is the same as x `xor` bit i
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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
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=bitSizebitSizeMaybe=Just.finiteBitSize
Since: base-4.7.0.0
countLeadingZeros :: 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 =finiteBitSizex - 1 -countLeadingZerosx
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 #
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
bitDefault :: (Bits a, Num a) => Int -> a #
testBitDefault :: (Bits a, Num a) => a -> Int -> Bool #
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 #
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 #
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 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