base-4.9.1.0: Basic libraries

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 #

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

Methods

(.&.) :: a -> a -> a infixl 7 #

Bitwise "and"

(.|.) :: a -> a -> a infixl 5 #

Bitwise "or"

xor :: a -> a -> a infixl 6 #

Bitwise "xor"

complement :: a -> a #

Reverse all the bits in the argument

shift :: a -> Int -> a infixl 8 #

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 #

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 #

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 #

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 #

x setBit i is the same as x .|. bit i

clearBit :: a -> Int -> a #

x clearBit i is the same as x .&. complement (bit i)

complementBit :: a -> Int -> a #

x complementBit i is the same as x xor bit i

testBit :: a -> Int -> Bool #

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 #

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 #

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 #

Return True if the argument is a signed type. The actual value of the argument is ignored

shiftL :: a -> Int -> a infixl 8 #

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 #

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 #

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 #

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 #

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 #

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 #

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

class Bits b => FiniteBits b where #

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 #

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 #

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 #

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

 # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods # Methods FiniteBits a => FiniteBits (Identity a) # Methods FiniteBits a => FiniteBits (Const k a b) # MethodsfiniteBitSize :: Const k a b -> Int #countLeadingZeros :: Const k a b -> Int #countTrailingZeros :: Const k a b -> Int #

bitDefault :: (Bits a, Num a) => Int -> a #

Default implementation for bit.

Note that: bitDefault i = 1 shiftL i

Since: 4.6.0.0

testBitDefault :: (Bits a, Num a) => a -> Int -> Bool #

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 #

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 #

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