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.

- Bits are numbered from 0 with bit 0 being the least significant bit.

(.&.), (.|.), 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 `

is a value with the *i*

th bit set and all other bits clear.*i*

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

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/7.10.3/docs/html/libraries/base-4.8.2.0/Data-Bits.html