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

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.

Minimal complete definition

(.&.), (.|.), xor, complement, (shift | shiftL, shiftR), (rotate | rotateL, rotateR), bitSize, bitSizeMaybe, isSigned, testBit, bit, popCount

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):

```
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 :: 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