base-4.11.0.0: 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

Documentation

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 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: 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 Source #

Interpret Bool as 1-bit bit-field

Since: 4.7.0.0

Instance details
Bits Int Source #

Since: 2.1

Instance details
Bits Int8 Source #

Since: 2.1

Instance details
Bits Int16 Source #

Since: 2.1

Instance details
Bits Int32 Source #

Since: 2.1

Instance details
Bits Int64 Source #

Since: 2.1

Instance details
Bits Integer Source #

Since: 2.1

Instance details
Bits Natural Source #

Since: 4.8.0.0

Instance details
Bits Word Source #

Since: 2.1

Instance details
Bits Word8 Source #

Since: 2.1

Instance details
Bits Word16 Source #

Since: 2.1

Instance details
Bits Word32 Source #

Since: 2.1

Instance details
Bits Word64 Source #

Since: 2.1

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

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: 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 Source #

Since: 4.7.0.0

Instance details
FiniteBits Int Source #

Since: 4.6.0.0

Instance details
FiniteBits Int8 Source #

Since: 4.6.0.0

Instance details
FiniteBits Int16 Source #

Since: 4.6.0.0

Instance details
FiniteBits Int32 Source #

Since: 4.6.0.0

Instance details
FiniteBits Int64 Source #

Since: 4.6.0.0

Instance details
FiniteBits Word Source #

Since: 4.6.0.0

Instance details
FiniteBits Word8 Source #

Since: 4.6.0.0

Instance details
FiniteBits Word16 Source #

Since: 4.6.0.0

Instance details
FiniteBits Word32 Source #

Since: 4.6.0.0

Instance details
FiniteBits Word64 Source #

Since: 4.6.0.0

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

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