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 |
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.
(.&.), (.|.), xor, complement, (shift | shiftL, shiftR), (rotate | rotateL, rotateR), bitSize, bitSizeMaybe, isSigned, testBit, bit, popCount
(.&.) :: 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 ==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: 4.7.0.0
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
.
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 n
th 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
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
.
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.
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
Bits Bool |
Interpret 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) | |
class Bits b => FiniteBits b where Source
The FiniteBits
class denotes types with a finite, fixed number of bits.
Since: 4.7.0.0
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
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