base-4.16.0.0: Basic libraries
Copyright(c) The University of Glasgow 2001
LicenseBSD-style (see the file libraries/base/LICENSE)
Maintainerlibraries@haskell.org
Stabilityexperimental
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Bits

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.

Synopsis

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.

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 #

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

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 GHC.Bits

Bits Int #

Since: base-2.1

Instance details

Defined in GHC.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 GHC.Bits

Bits Natural #

Since: base-4.8.0

Instance details

Defined in GHC.Bits

Bits Word #

Since: base-2.1

Instance details

Defined in GHC.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 CBool # 
Instance details

Defined in Foreign.C.Types

Bits CChar # 
Instance details

Defined in Foreign.C.Types

Bits CInt # 
Instance details

Defined in Foreign.C.Types

Bits CIntMax # 
Instance details

Defined in Foreign.C.Types

Bits CIntPtr # 
Instance details

Defined in Foreign.C.Types

Bits CLLong # 
Instance details

Defined in Foreign.C.Types

Bits CLong # 
Instance details

Defined in Foreign.C.Types

Bits CPtrdiff # 
Instance details

Defined in Foreign.C.Types

Bits CSChar # 
Instance details

Defined in Foreign.C.Types

Bits CShort # 
Instance details

Defined in Foreign.C.Types

Bits CSigAtomic # 
Instance details

Defined in Foreign.C.Types

Bits CSize # 
Instance details

Defined in Foreign.C.Types

Bits CUChar # 
Instance details

Defined in Foreign.C.Types

Bits CUInt # 
Instance details

Defined in Foreign.C.Types

Bits CUIntMax # 
Instance details

Defined in Foreign.C.Types

Bits CUIntPtr # 
Instance details

Defined in Foreign.C.Types

Bits CULLong # 
Instance details

Defined in Foreign.C.Types

Bits CULong # 
Instance details

Defined in Foreign.C.Types

Bits CUShort # 
Instance details

Defined in Foreign.C.Types

Bits CWchar # 
Instance details

Defined in Foreign.C.Types

Bits CBlkCnt # 
Instance details

Defined in System.Posix.Types

Bits CBlkSize # 
Instance details

Defined in System.Posix.Types

Bits CClockId # 
Instance details

Defined in System.Posix.Types

Bits CDev # 
Instance details

Defined in System.Posix.Types

Bits CFsBlkCnt # 
Instance details

Defined in System.Posix.Types

Bits CFsFilCnt # 
Instance details

Defined in System.Posix.Types

Bits CGid # 
Instance details

Defined in System.Posix.Types

Bits CId # 
Instance details

Defined in System.Posix.Types

Bits CIno # 
Instance details

Defined in System.Posix.Types

Bits CKey # 
Instance details

Defined in System.Posix.Types

Bits CMode # 
Instance details

Defined in System.Posix.Types

Bits CNfds # 
Instance details

Defined in System.Posix.Types

Bits CNlink # 
Instance details

Defined in System.Posix.Types

Bits COff # 
Instance details

Defined in System.Posix.Types

Bits CPid # 
Instance details

Defined in System.Posix.Types

Bits CRLim # 
Instance details

Defined in System.Posix.Types

Bits CSocklen # 
Instance details

Defined in System.Posix.Types

Bits CSsize # 
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 Fd # 
Instance details

Defined in System.Posix.Types

Bits a => Bits (And a) #

Since: base-4.16

Instance details

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 #

zeroBits :: And a Source #

bit :: 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 #

rotateR :: And a -> Int -> And a Source #

popCount :: And a -> Int Source #

Bits a => Bits (Iff a) #

Since: base-4.16

Instance details

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 #

zeroBits :: Iff a Source #

bit :: 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 #

rotateR :: Iff a -> Int -> Iff a Source #

popCount :: Iff a -> Int Source #

Bits a => Bits (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(.&.) :: Ior a -> Ior a -> Ior a Source #

(.|.) :: Ior a -> Ior a -> Ior a Source #

xor :: Ior a -> Ior a -> Ior a Source #

complement :: Ior a -> Ior a Source #

shift :: Ior a -> Int -> Ior a Source #

rotate :: Ior a -> Int -> Ior a Source #

zeroBits :: Ior a Source #

bit :: Int -> Ior a Source #

setBit :: Ior a -> Int -> Ior a Source #

clearBit :: Ior a -> Int -> Ior a Source #

complementBit :: Ior a -> Int -> Ior a Source #

testBit :: Ior a -> Int -> Bool Source #

bitSizeMaybe :: Ior a -> Maybe Int Source #

bitSize :: Ior a -> Int Source #

isSigned :: Ior a -> Bool Source #

shiftL :: Ior a -> Int -> Ior a Source #

unsafeShiftL :: Ior a -> Int -> Ior a Source #

shiftR :: Ior a -> Int -> Ior a Source #

unsafeShiftR :: Ior a -> Int -> Ior a Source #

rotateL :: Ior a -> Int -> Ior a Source #

rotateR :: Ior a -> Int -> Ior a Source #

popCount :: Ior a -> Int Source #

Bits a => Bits (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(.&.) :: Xor a -> Xor a -> Xor a Source #

(.|.) :: Xor a -> Xor a -> Xor a Source #

xor :: Xor a -> Xor a -> Xor a Source #

complement :: Xor a -> Xor a Source #

shift :: Xor a -> Int -> Xor a Source #

rotate :: Xor a -> Int -> Xor a Source #

zeroBits :: Xor a Source #

bit :: Int -> Xor a Source #

setBit :: Xor a -> Int -> Xor a Source #

clearBit :: Xor a -> Int -> Xor a Source #

complementBit :: Xor a -> Int -> Xor a Source #

testBit :: Xor a -> Int -> Bool Source #

bitSizeMaybe :: Xor a -> Maybe Int Source #

bitSize :: Xor a -> Int Source #

isSigned :: Xor a -> Bool Source #

shiftL :: Xor a -> Int -> Xor a Source #

unsafeShiftL :: Xor a -> Int -> Xor a Source #

shiftR :: Xor a -> Int -> Xor a Source #

unsafeShiftR :: Xor a -> Int -> Xor a Source #

rotateL :: Xor a -> Int -> Xor a Source #

rotateR :: Xor a -> Int -> Xor a Source #

popCount :: Xor a -> Int Source #

Bits a => Bits (Down a) #

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Methods

(.&.) :: Down a -> Down a -> Down a Source #

(.|.) :: Down a -> Down a -> Down a Source #

xor :: Down a -> Down a -> Down a Source #

complement :: Down a -> Down a Source #

shift :: Down a -> Int -> Down a Source #

rotate :: Down a -> Int -> Down a Source #

zeroBits :: Down a Source #

bit :: Int -> Down a Source #

setBit :: Down a -> Int -> Down a Source #

clearBit :: Down a -> Int -> Down a Source #

complementBit :: Down a -> Int -> Down a Source #

testBit :: Down a -> Int -> Bool Source #

bitSizeMaybe :: Down a -> Maybe Int Source #

bitSize :: Down a -> Int Source #

isSigned :: Down a -> Bool Source #

shiftL :: Down a -> Int -> Down a Source #

unsafeShiftL :: Down a -> Int -> Down a Source #

shiftR :: Down a -> Int -> Down a Source #

unsafeShiftR :: Down a -> Int -> Down a Source #

rotateL :: Down a -> Int -> Down a Source #

rotateR :: Down a -> Int -> Down a Source #

popCount :: Down a -> Int Source #

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 GHC.Bits

FiniteBits Int #

Since: base-4.6.0.0

Instance details

Defined in GHC.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 GHC.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 CBool # 
Instance details

Defined in Foreign.C.Types

FiniteBits CChar # 
Instance details

Defined in Foreign.C.Types

FiniteBits CInt # 
Instance details

Defined in Foreign.C.Types

FiniteBits CIntMax # 
Instance details

Defined in Foreign.C.Types

FiniteBits CIntPtr # 
Instance details

Defined in Foreign.C.Types

FiniteBits CLLong # 
Instance details

Defined in Foreign.C.Types

FiniteBits CLong # 
Instance details

Defined in Foreign.C.Types

FiniteBits CPtrdiff # 
Instance details

Defined in Foreign.C.Types

FiniteBits CSChar # 
Instance details

Defined in Foreign.C.Types

FiniteBits CShort # 
Instance details

Defined in Foreign.C.Types

FiniteBits CSigAtomic # 
Instance details

Defined in Foreign.C.Types

FiniteBits CSize # 
Instance details

Defined in Foreign.C.Types

FiniteBits CUChar # 
Instance details

Defined in Foreign.C.Types

FiniteBits CUInt # 
Instance details

Defined in Foreign.C.Types

FiniteBits CUIntMax # 
Instance details

Defined in Foreign.C.Types

FiniteBits CUIntPtr # 
Instance details

Defined in Foreign.C.Types

FiniteBits CULLong # 
Instance details

Defined in Foreign.C.Types

FiniteBits CULong # 
Instance details

Defined in Foreign.C.Types

FiniteBits CUShort # 
Instance details

Defined in Foreign.C.Types

FiniteBits CWchar # 
Instance details

Defined in Foreign.C.Types

FiniteBits CBlkCnt # 
Instance details

Defined in System.Posix.Types

FiniteBits CBlkSize # 
Instance details

Defined in System.Posix.Types

FiniteBits CClockId # 
Instance details

Defined in System.Posix.Types

FiniteBits CDev # 
Instance details

Defined in System.Posix.Types

FiniteBits CFsBlkCnt # 
Instance details

Defined in System.Posix.Types

FiniteBits CFsFilCnt # 
Instance details

Defined in System.Posix.Types

FiniteBits CGid # 
Instance details

Defined in System.Posix.Types

FiniteBits CId # 
Instance details

Defined in System.Posix.Types

FiniteBits CIno # 
Instance details

Defined in System.Posix.Types

FiniteBits CKey # 
Instance details

Defined in System.Posix.Types

FiniteBits CMode # 
Instance details

Defined in System.Posix.Types

FiniteBits CNfds # 
Instance details

Defined in System.Posix.Types

FiniteBits CNlink # 
Instance details

Defined in System.Posix.Types

FiniteBits COff # 
Instance details

Defined in System.Posix.Types

FiniteBits CPid # 
Instance details

Defined in System.Posix.Types

FiniteBits CRLim # 
Instance details

Defined in System.Posix.Types

FiniteBits CSocklen # 
Instance details

Defined in System.Posix.Types

FiniteBits CSsize # 
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 Fd # 
Instance details

Defined in System.Posix.Types

FiniteBits a => FiniteBits (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

FiniteBits a => FiniteBits (Iff a) #

Since: base-4.16

Instance details

Defined in Data.Bits

FiniteBits a => FiniteBits (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

FiniteBits a => FiniteBits (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

FiniteBits a => FiniteBits (Down a) #

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

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

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 == 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

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

Newtypes

newtype And a Source #

Monoid under bitwise AND.

>>> getAnd (And 0xab <> And 0x12) :: Word8
2

Since: base-4.16

Constructors

And 

Fields

Instances

Instances details
Bounded a => Bounded (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Enum a => Enum (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

succ :: And a -> And a Source #

pred :: And a -> And a Source #

toEnum :: Int -> And a Source #

fromEnum :: And a -> Int Source #

enumFrom :: And a -> [And a] Source #

enumFromThen :: And a -> And a -> [And a] Source #

enumFromTo :: And a -> And a -> [And a] Source #

enumFromThenTo :: And a -> And a -> And a -> [And a] Source #

Eq a => Eq (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(==) :: And a -> And a -> Bool Source #

(/=) :: And a -> And a -> Bool Source #

Read a => Read (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Show a => Show (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

showsPrec :: Int -> And a -> ShowS Source #

show :: And a -> String Source #

showList :: [And a] -> ShowS Source #

Bits a => Semigroup (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: And a -> And a -> And a Source #

sconcat :: NonEmpty (And a) -> And a Source #

stimes :: Integral b => b -> And a -> And a Source #

FiniteBits a => Monoid (And a) #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: And a Source #

mappend :: And a -> And a -> And a Source #

mconcat :: [And a] -> And a Source #

Bits a => Bits (And a) #

Since: base-4.16

Instance details

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 #

zeroBits :: And a Source #

bit :: 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 #

rotateR :: And a -> Int -> And a Source #

popCount :: And a -> Int Source #

FiniteBits a => FiniteBits (And a) #

Since: base-4.16

Instance details

Defined in Data.Bits

newtype Ior a Source #

Monoid under bitwise inclusive OR.

>>> getIor (Ior 0xab <> Ior 0x12) :: Word8
187

Since: base-4.16

Constructors

Ior 

Fields

Instances

Instances details
Bounded a => Bounded (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Enum a => Enum (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

succ :: Ior a -> Ior a Source #

pred :: Ior a -> Ior a Source #

toEnum :: Int -> Ior a Source #

fromEnum :: Ior a -> Int Source #

enumFrom :: Ior a -> [Ior a] Source #

enumFromThen :: Ior a -> Ior a -> [Ior a] Source #

enumFromTo :: Ior a -> Ior a -> [Ior a] Source #

enumFromThenTo :: Ior a -> Ior a -> Ior a -> [Ior a] Source #

Eq a => Eq (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(==) :: Ior a -> Ior a -> Bool Source #

(/=) :: Ior a -> Ior a -> Bool Source #

Read a => Read (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Show a => Show (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

showsPrec :: Int -> Ior a -> ShowS Source #

show :: Ior a -> String Source #

showList :: [Ior a] -> ShowS Source #

Bits a => Semigroup (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: Ior a -> Ior a -> Ior a Source #

sconcat :: NonEmpty (Ior a) -> Ior a Source #

stimes :: Integral b => b -> Ior a -> Ior a Source #

Bits a => Monoid (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Ior a Source #

mappend :: Ior a -> Ior a -> Ior a Source #

mconcat :: [Ior a] -> Ior a Source #

Bits a => Bits (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(.&.) :: Ior a -> Ior a -> Ior a Source #

(.|.) :: Ior a -> Ior a -> Ior a Source #

xor :: Ior a -> Ior a -> Ior a Source #

complement :: Ior a -> Ior a Source #

shift :: Ior a -> Int -> Ior a Source #

rotate :: Ior a -> Int -> Ior a Source #

zeroBits :: Ior a Source #

bit :: Int -> Ior a Source #

setBit :: Ior a -> Int -> Ior a Source #

clearBit :: Ior a -> Int -> Ior a Source #

complementBit :: Ior a -> Int -> Ior a Source #

testBit :: Ior a -> Int -> Bool Source #

bitSizeMaybe :: Ior a -> Maybe Int Source #

bitSize :: Ior a -> Int Source #

isSigned :: Ior a -> Bool Source #

shiftL :: Ior a -> Int -> Ior a Source #

unsafeShiftL :: Ior a -> Int -> Ior a Source #

shiftR :: Ior a -> Int -> Ior a Source #

unsafeShiftR :: Ior a -> Int -> Ior a Source #

rotateL :: Ior a -> Int -> Ior a Source #

rotateR :: Ior a -> Int -> Ior a Source #

popCount :: Ior a -> Int Source #

FiniteBits a => FiniteBits (Ior a) #

Since: base-4.16

Instance details

Defined in Data.Bits

newtype Xor a Source #

Monoid under bitwise XOR.

>>> getXor (Xor 0xab <> 0x12) :: Word8
185

Since: base-4.16

Constructors

Xor 

Fields

Instances

Instances details
Bounded a => Bounded (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Enum a => Enum (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

succ :: Xor a -> Xor a Source #

pred :: Xor a -> Xor a Source #

toEnum :: Int -> Xor a Source #

fromEnum :: Xor a -> Int Source #

enumFrom :: Xor a -> [Xor a] Source #

enumFromThen :: Xor a -> Xor a -> [Xor a] Source #

enumFromTo :: Xor a -> Xor a -> [Xor a] Source #

enumFromThenTo :: Xor a -> Xor a -> Xor a -> [Xor a] Source #

Eq a => Eq (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(==) :: Xor a -> Xor a -> Bool Source #

(/=) :: Xor a -> Xor a -> Bool Source #

Read a => Read (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Show a => Show (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

showsPrec :: Int -> Xor a -> ShowS Source #

show :: Xor a -> String Source #

showList :: [Xor a] -> ShowS Source #

Bits a => Semigroup (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: Xor a -> Xor a -> Xor a Source #

sconcat :: NonEmpty (Xor a) -> Xor a Source #

stimes :: Integral b => b -> Xor a -> Xor a Source #

Bits a => Monoid (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Xor a Source #

mappend :: Xor a -> Xor a -> Xor a Source #

mconcat :: [Xor a] -> Xor a Source #

Bits a => Bits (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(.&.) :: Xor a -> Xor a -> Xor a Source #

(.|.) :: Xor a -> Xor a -> Xor a Source #

xor :: Xor a -> Xor a -> Xor a Source #

complement :: Xor a -> Xor a Source #

shift :: Xor a -> Int -> Xor a Source #

rotate :: Xor a -> Int -> Xor a Source #

zeroBits :: Xor a Source #

bit :: Int -> Xor a Source #

setBit :: Xor a -> Int -> Xor a Source #

clearBit :: Xor a -> Int -> Xor a Source #

complementBit :: Xor a -> Int -> Xor a Source #

testBit :: Xor a -> Int -> Bool Source #

bitSizeMaybe :: Xor a -> Maybe Int Source #

bitSize :: Xor a -> Int Source #

isSigned :: Xor a -> Bool Source #

shiftL :: Xor a -> Int -> Xor a Source #

unsafeShiftL :: Xor a -> Int -> Xor a Source #

shiftR :: Xor a -> Int -> Xor a Source #

unsafeShiftR :: Xor a -> Int -> Xor a Source #

rotateL :: Xor a -> Int -> Xor a Source #

rotateR :: Xor a -> Int -> Xor a Source #

popCount :: Xor a -> Int Source #

FiniteBits a => FiniteBits (Xor a) #

Since: base-4.16

Instance details

Defined in Data.Bits

newtype Iff a Source #

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

Constructors

Iff 

Fields

Instances

Instances details
Bounded a => Bounded (Iff a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Enum a => Enum (Iff a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

succ :: Iff a -> Iff a Source #

pred :: Iff a -> Iff a Source #

toEnum :: Int -> Iff a Source #

fromEnum :: Iff a -> Int Source #

enumFrom :: Iff a -> [Iff a] Source #

enumFromThen :: Iff a -> Iff a -> [Iff a] Source #

enumFromTo :: Iff a -> Iff a -> [Iff a] Source #

enumFromThenTo :: Iff a -> Iff a -> Iff a -> [Iff a] Source #

Eq a => Eq (Iff a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(==) :: Iff a -> Iff a -> Bool Source #

(/=) :: Iff a -> Iff a -> Bool Source #

Read a => Read (Iff a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Show a => Show (Iff a) #

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

showsPrec :: Int -> Iff a -> ShowS Source #

show :: Iff a -> String Source #

showList :: [Iff a] -> ShowS Source #

FiniteBits a => Semigroup (Iff a) #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: Iff a -> Iff a -> Iff a Source #

sconcat :: NonEmpty (Iff a) -> Iff a Source #

stimes :: Integral b => b -> Iff a -> Iff a Source #

FiniteBits a => Monoid (Iff a) #

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Iff a Source #

mappend :: Iff a -> Iff a -> Iff a Source #

mconcat :: [Iff a] -> Iff a Source #

Bits a => Bits (Iff a) #

Since: base-4.16

Instance details

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 #

zeroBits :: Iff a Source #

bit :: 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 #

rotateR :: Iff a -> Int -> Iff a Source #

popCount :: Iff a -> Int Source #

FiniteBits a => FiniteBits (Iff a) #

Since: base-4.16

Instance details

Defined in Data.Bits