planet-mitchell-0.0.0: Planet Mitchell

Safe HaskellSafe
LanguageHaskell2010

Bits

Contents

Synopsis

Bits

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.

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):

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: base-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: base-4.7.0.0

bitSize :: a -> Int #

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: base-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 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: base-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: base-4.5.0.0

Instances
Bits Bool

Interpret Bool as 1-bit bit-field

Since: base-4.7.0.0

Instance details

Defined in Data.Bits

Bits Int

Since: base-2.1

Instance details

Defined in Data.Bits

Methods

(.&.) :: Int -> Int -> Int #

(.|.) :: Int -> Int -> Int #

xor :: Int -> Int -> Int #

complement :: Int -> Int #

shift :: Int -> Int -> Int #

rotate :: Int -> Int -> Int #

zeroBits :: Int #

bit :: Int -> Int #

setBit :: Int -> Int -> Int #

clearBit :: Int -> Int -> Int #

complementBit :: Int -> Int -> Int #

testBit :: Int -> Int -> Bool #

bitSizeMaybe :: Int -> Maybe Int #

bitSize :: Int -> Int #

isSigned :: Int -> Bool #

shiftL :: Int -> Int -> Int #

unsafeShiftL :: Int -> Int -> Int #

shiftR :: Int -> Int -> Int #

unsafeShiftR :: Int -> Int -> Int #

rotateL :: Int -> Int -> Int #

rotateR :: Int -> Int -> Int #

popCount :: Int -> Int #

Bits Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Bits Integer

Since: base-2.1

Instance details

Defined in Data.Bits

Bits Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Bits Word

Since: base-2.1

Instance details

Defined in Data.Bits

Bits Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Bits Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Bits Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Bits Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Bits CDev 
Instance details

Defined in System.Posix.Types

Bits CIno 
Instance details

Defined in System.Posix.Types

Bits CMode 
Instance details

Defined in System.Posix.Types

Bits COff 
Instance details

Defined in System.Posix.Types

Bits CPid 
Instance details

Defined in System.Posix.Types

Bits CSsize 
Instance details

Defined in System.Posix.Types

Bits CGid 
Instance details

Defined in System.Posix.Types

Bits CNlink 
Instance details

Defined in System.Posix.Types

Bits CUid 
Instance details

Defined in System.Posix.Types

Bits CTcflag 
Instance details

Defined in System.Posix.Types

Bits CRLim 
Instance details

Defined in System.Posix.Types

Bits CBlkSize 
Instance details

Defined in System.Posix.Types

Bits CBlkCnt 
Instance details

Defined in System.Posix.Types

Bits CClockId 
Instance details

Defined in System.Posix.Types

Bits CFsBlkCnt 
Instance details

Defined in System.Posix.Types

Bits CFsFilCnt 
Instance details

Defined in System.Posix.Types

Bits CId 
Instance details

Defined in System.Posix.Types

Methods

(.&.) :: CId -> CId -> CId #

(.|.) :: CId -> CId -> CId #

xor :: CId -> CId -> CId #

complement :: CId -> CId #

shift :: CId -> Int -> CId #

rotate :: CId -> Int -> CId #

zeroBits :: CId #

bit :: Int -> CId #

setBit :: CId -> Int -> CId #

clearBit :: CId -> Int -> CId #

complementBit :: CId -> Int -> CId #

testBit :: CId -> Int -> Bool #

bitSizeMaybe :: CId -> Maybe Int #

bitSize :: CId -> Int #

isSigned :: CId -> Bool #

shiftL :: CId -> Int -> CId #

unsafeShiftL :: CId -> Int -> CId #

shiftR :: CId -> Int -> CId #

unsafeShiftR :: CId -> Int -> CId #

rotateL :: CId -> Int -> CId #

rotateR :: CId -> Int -> CId #

popCount :: CId -> Int #

Bits CKey 
Instance details

Defined in System.Posix.Types

Bits Fd 
Instance details

Defined in System.Posix.Types

Methods

(.&.) :: Fd -> Fd -> Fd #

(.|.) :: Fd -> Fd -> Fd #

xor :: Fd -> Fd -> Fd #

complement :: Fd -> Fd #

shift :: Fd -> Int -> Fd #

rotate :: Fd -> Int -> Fd #

zeroBits :: Fd #

bit :: Int -> Fd #

setBit :: Fd -> Int -> Fd #

clearBit :: Fd -> Int -> Fd #

complementBit :: Fd -> Int -> Fd #

testBit :: Fd -> Int -> Bool #

bitSizeMaybe :: Fd -> Maybe Int #

bitSize :: Fd -> Int #

isSigned :: Fd -> Bool #

shiftL :: Fd -> Int -> Fd #

unsafeShiftL :: Fd -> Int -> Fd #

shiftR :: Fd -> Int -> Fd #

unsafeShiftR :: Fd -> Int -> Fd #

rotateL :: Fd -> Int -> Fd #

rotateR :: Fd -> Int -> Fd #

popCount :: Fd -> Int #

Bits CChar 
Instance details

Defined in Foreign.C.Types

Bits CSChar 
Instance details

Defined in Foreign.C.Types

Bits CUChar 
Instance details

Defined in Foreign.C.Types

Bits CShort 
Instance details

Defined in Foreign.C.Types

Bits CUShort 
Instance details

Defined in Foreign.C.Types

Bits CInt 
Instance details

Defined in Foreign.C.Types

Bits CUInt 
Instance details

Defined in Foreign.C.Types

Bits CLong 
Instance details

Defined in Foreign.C.Types

Bits CULong 
Instance details

Defined in Foreign.C.Types

Bits CLLong 
Instance details

Defined in Foreign.C.Types

Bits CULLong 
Instance details

Defined in Foreign.C.Types

Bits CBool 
Instance details

Defined in Foreign.C.Types

Bits CPtrdiff 
Instance details

Defined in Foreign.C.Types

Bits CSize 
Instance details

Defined in Foreign.C.Types

Bits CWchar 
Instance details

Defined in Foreign.C.Types

Bits CSigAtomic 
Instance details

Defined in Foreign.C.Types

Bits CIntPtr 
Instance details

Defined in Foreign.C.Types

Bits CUIntPtr 
Instance details

Defined in Foreign.C.Types

Bits CIntMax 
Instance details

Defined in Foreign.C.Types

Bits CUIntMax 
Instance details

Defined in Foreign.C.Types

Bits WordPtr 
Instance details

Defined in Foreign.Ptr

Bits IntPtr 
Instance details

Defined in Foreign.Ptr

() :=> (Bits Bool) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Bits Bool #

() :=> (Bits Int) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Bits Int #

() :=> (Bits Integer) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Bits Integer #

() :=> (Bits Natural) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Bits Natural #

() :=> (Bits Word) 
Instance details

Defined in Data.Constraint

Methods

ins :: () :- Bits Word #

Bits a => Bits (Identity a) 
Instance details

Defined in Data.Functor.Identity

Class (Eq a) (Bits a) 
Instance details

Defined in Data.Constraint

Methods

cls :: Bits a :- Eq a #

(Bits a) :=> (Bits (Identity a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Bits a :- Bits (Identity a) #

(Bits a) :=> (Bits (Const a b)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Bits a :- Bits (Const a b) #

Bits a => Bits (Const a b) 
Instance details

Defined in Data.Functor.Const

Methods

(.&.) :: Const a b -> Const a b -> Const a b #

(.|.) :: Const a b -> Const a b -> Const a b #

xor :: Const a b -> Const a b -> Const a b #

complement :: Const a b -> Const a b #

shift :: Const a b -> Int -> Const a b #

rotate :: Const a b -> Int -> Const a b #

zeroBits :: Const a b #

bit :: Int -> Const a b #

setBit :: Const a b -> Int -> Const a b #

clearBit :: Const a b -> Int -> Const a b #

complementBit :: Const a b -> Int -> Const a b #

testBit :: Const a b -> Int -> Bool #

bitSizeMaybe :: Const a b -> Maybe Int #

bitSize :: Const a b -> Int #

isSigned :: Const a b -> Bool #

shiftL :: Const a b -> Int -> Const a b #

unsafeShiftL :: Const a b -> Int -> Const a b #

shiftR :: Const a b -> Int -> Const a b #

unsafeShiftR :: Const a b -> Int -> Const a b #

rotateL :: Const a b -> Int -> Const a b #

rotateR :: Const a b -> Int -> Const a b #

popCount :: Const a b -> Int #

Bits a => Bits (Tagged s a) 
Instance details

Defined in Data.Tagged

Methods

(.&.) :: Tagged s a -> Tagged s a -> Tagged s a #

(.|.) :: Tagged s a -> Tagged s a -> Tagged s a #

xor :: Tagged s a -> Tagged s a -> Tagged s a #

complement :: Tagged s a -> Tagged s a #

shift :: Tagged s a -> Int -> Tagged s a #

rotate :: Tagged s a -> Int -> Tagged s a #

zeroBits :: Tagged s a #

bit :: Int -> Tagged s a #

setBit :: Tagged s a -> Int -> Tagged s a #

clearBit :: Tagged s a -> Int -> Tagged s a #

complementBit :: Tagged s a -> Int -> Tagged s a #

testBit :: Tagged s a -> Int -> Bool #

bitSizeMaybe :: Tagged s a -> Maybe Int #

bitSize :: Tagged s a -> Int #

isSigned :: Tagged s a -> Bool #

shiftL :: Tagged s a -> Int -> Tagged s a #

unsafeShiftL :: Tagged s a -> Int -> Tagged s a #

shiftR :: Tagged s a -> Int -> Tagged s a #

unsafeShiftR :: Tagged s a -> Int -> Tagged s a #

rotateL :: Tagged s a -> Int -> Tagged s a #

rotateR :: Tagged s a -> Int -> Tagged s a #

popCount :: Tagged s a -> Int #

srl :: Bits b => b -> Int -> b #

Shift Right Logical (i.e., without sign extension)

NB: When used on negative Integers, hilarity may ensue.

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: base-4.8.0.0

class Bits b => FiniteBits b where #

The FiniteBits class denotes types with a finite, fixed number of bits.

Since: base-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: base-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: base-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: base-4.8.0.0

Instances
FiniteBits Bool

Since: base-4.7.0.0

Instance details

Defined in Data.Bits

FiniteBits Int

Since: base-4.6.0.0

Instance details

Defined in Data.Bits

FiniteBits Int8

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Int16

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Int32

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Int64

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

FiniteBits Word

Since: base-4.6.0.0

Instance details

Defined in Data.Bits

FiniteBits Word8

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits Word16

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits Word32

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits Word64

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

FiniteBits CDev 
Instance details

Defined in System.Posix.Types

FiniteBits CIno 
Instance details

Defined in System.Posix.Types

FiniteBits CMode 
Instance details

Defined in System.Posix.Types

FiniteBits COff 
Instance details

Defined in System.Posix.Types

FiniteBits CPid 
Instance details

Defined in System.Posix.Types

FiniteBits CSsize 
Instance details

Defined in System.Posix.Types

FiniteBits CGid 
Instance details

Defined in System.Posix.Types

FiniteBits CNlink 
Instance details

Defined in System.Posix.Types

FiniteBits CUid 
Instance details

Defined in System.Posix.Types

FiniteBits CTcflag 
Instance details

Defined in System.Posix.Types

FiniteBits CRLim 
Instance details

Defined in System.Posix.Types

FiniteBits CBlkSize 
Instance details

Defined in System.Posix.Types

FiniteBits CBlkCnt 
Instance details

Defined in System.Posix.Types

FiniteBits CClockId 
Instance details

Defined in System.Posix.Types

FiniteBits CFsBlkCnt 
Instance details

Defined in System.Posix.Types

FiniteBits CFsFilCnt 
Instance details

Defined in System.Posix.Types

FiniteBits CId 
Instance details

Defined in System.Posix.Types

FiniteBits CKey 
Instance details

Defined in System.Posix.Types

FiniteBits Fd 
Instance details

Defined in System.Posix.Types

FiniteBits CChar 
Instance details

Defined in Foreign.C.Types

FiniteBits CSChar 
Instance details

Defined in Foreign.C.Types

FiniteBits CUChar 
Instance details

Defined in Foreign.C.Types

FiniteBits CShort 
Instance details

Defined in Foreign.C.Types

FiniteBits CUShort 
Instance details

Defined in Foreign.C.Types

FiniteBits CInt 
Instance details

Defined in Foreign.C.Types

FiniteBits CUInt 
Instance details

Defined in Foreign.C.Types

FiniteBits CLong 
Instance details

Defined in Foreign.C.Types

FiniteBits CULong 
Instance details

Defined in Foreign.C.Types

FiniteBits CLLong 
Instance details

Defined in Foreign.C.Types

FiniteBits CULLong 
Instance details

Defined in Foreign.C.Types

FiniteBits CBool 
Instance details

Defined in Foreign.C.Types

FiniteBits CPtrdiff 
Instance details

Defined in Foreign.C.Types

FiniteBits CSize 
Instance details

Defined in Foreign.C.Types

FiniteBits CWchar 
Instance details

Defined in Foreign.C.Types

FiniteBits CSigAtomic 
Instance details

Defined in Foreign.C.Types

FiniteBits CIntPtr 
Instance details

Defined in Foreign.C.Types

FiniteBits CUIntPtr 
Instance details

Defined in Foreign.C.Types

FiniteBits CIntMax 
Instance details

Defined in Foreign.C.Types

FiniteBits CUIntMax 
Instance details

Defined in Foreign.C.Types

FiniteBits WordPtr 
Instance details

Defined in Foreign.Ptr

FiniteBits IntPtr 
Instance details

Defined in Foreign.Ptr

FiniteBits a => FiniteBits (Identity a) 
Instance details

Defined in Data.Functor.Identity

FiniteBits a => FiniteBits (Const a b) 
Instance details

Defined in Data.Functor.Const

FiniteBits a => FiniteBits (Tagged s a) 
Instance details

Defined in Data.Tagged

class (Num t, FiniteBits t) => Ranked t where #

Minimal complete definition

nlz

Methods

lsb :: t -> Int #

Calculate the least significant set bit using a debruijn multiplication table. NB: The result of this function is undefined when given 0.

rank :: t -> Int #

Calculate the number of trailing 0 bits.

nlz :: t -> Int #

Calculate the number of leading zeros.

Instances
Ranked Int8 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Int8 -> Int #

rank :: Int8 -> Int #

nlz :: Int8 -> Int #

Ranked Int16 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Int16 -> Int #

rank :: Int16 -> Int #

nlz :: Int16 -> Int #

Ranked Int32 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Int32 -> Int #

rank :: Int32 -> Int #

nlz :: Int32 -> Int #

Ranked Int64 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Int64 -> Int #

rank :: Int64 -> Int #

nlz :: Int64 -> Int #

Ranked Word8 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Word8 -> Int #

rank :: Word8 -> Int #

nlz :: Word8 -> Int #

Ranked Word16 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Word16 -> Int #

rank :: Word16 -> Int #

nlz :: Word16 -> Int #

Ranked Word32 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Word32 -> Int #

rank :: Word32 -> Int #

nlz :: Word32 -> Int #

Ranked Word64 
Instance details

Defined in Data.Bits.Extras

Methods

lsb :: Word64 -> Int #

rank :: Word64 -> Int #

nlz :: Word64 -> Int #

msb :: Ranked t => t -> Int #

Calculate the most significant set bit.

Default Bits implementations

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

Default implementation for bit.

Note that: bitDefault i = 1 shiftL i

Since: base-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: base-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: base-4.6.0.0