base-4.8.1.0: 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 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.

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 
Bits Int Source 
Bits Int8 Source 
Bits Int16 Source 
Bits Int32 Source 
Bits Int64 Source 
Bits Integer Source 
Bits Word Source 
Bits Word8 Source 
Bits Word16 Source 
Bits Word32 Source 
Bits Word64 Source 
Bits CUIntMax Source 
Bits CIntMax Source 
Bits CUIntPtr Source 
Bits CIntPtr Source 
Bits CSigAtomic Source 
Bits CWchar Source 
Bits CSize Source 
Bits CPtrdiff Source 
Bits CULLong Source 
Bits CLLong Source 
Bits CULong Source 
Bits CLong Source 
Bits CUInt Source 
Bits CInt Source 
Bits CUShort Source 
Bits CShort Source 
Bits CUChar Source 
Bits CSChar Source 
Bits CChar Source 
Bits IntPtr Source 
Bits WordPtr Source 
Bits Fd Source 
Bits CRLim Source 
Bits CTcflag Source 
Bits CUid Source 
Bits CNlink Source 
Bits CGid Source 
Bits CSsize Source 
Bits CPid Source 
Bits COff Source 
Bits CMode Source 
Bits CIno Source 
Bits CDev Source 
Bits Natural 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 
FiniteBits Int Source 
FiniteBits Int8 Source 
FiniteBits Int16 Source 
FiniteBits Int32 Source 
FiniteBits Int64 Source 
FiniteBits Word Source 
FiniteBits Word8 Source 
FiniteBits Word16 Source 
FiniteBits Word32 Source 
FiniteBits Word64 Source 
FiniteBits CUIntMax Source 
FiniteBits CIntMax Source 
FiniteBits CUIntPtr Source 
FiniteBits CIntPtr Source 
FiniteBits CSigAtomic Source 
FiniteBits CWchar Source 
FiniteBits CSize Source 
FiniteBits CPtrdiff Source 
FiniteBits CULLong Source 
FiniteBits CLLong Source 
FiniteBits CULong Source 
FiniteBits CLong Source 
FiniteBits CUInt Source 
FiniteBits CInt Source 
FiniteBits CUShort Source 
FiniteBits CShort Source 
FiniteBits CUChar Source 
FiniteBits CSChar Source 
FiniteBits CChar Source 
FiniteBits IntPtr Source 
FiniteBits WordPtr Source 
FiniteBits Fd Source 
FiniteBits CRLim Source 
FiniteBits CTcflag Source 
FiniteBits CUid Source 
FiniteBits CNlink Source 
FiniteBits CGid Source 
FiniteBits CSsize Source 
FiniteBits CPid Source 
FiniteBits COff Source 
FiniteBits CMode Source 
FiniteBits CIno Source 
FiniteBits CDev Source 

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