bv-little-1.1.0: Efficient little-endian bit vector library

Copyright (c) Alex Washburn 2018 BSD-style github@recursion.ninja provisional portable Trustworthy Haskell2010

Data.BitVector.LittleEndian

Description

A bit vector similar to Data.BitVector from the bv, however the endianness is reversed. This module defines little-endian pseudo–size-polymorphic bit vectors.

Little-endian bit vectors are isomorphic to a [Bool] with the least significant bit at the head of the list and the most significant bit at the end of the list. Consequently, the endianness of a bit vector affects the semantics of the following typeclasses:

• Bits
• FiniteBits
• Semigroup
• Monoid
• MonoAdjustable
• MonoIndexable
• MonoKeyed
• MonoLookup
• MonoFoldable
• MonoFoldableWithKey
• MonoTraversable
• MonoTraversableWithKey
• MonoZipWithKey

For an implementation of bit vectors which are isomorphic to a [Bool] with the most significant bit at the head of the list and the least significant bit at the end of the list, use the bv package.

This module does not define numeric instances for BitVector. This is intentional! To interact with a bit vector as an Integral value, convert the BitVector using either toSignedNumber or toUnsignedNumber.

This module defines rank and select operations for BitVector as a succinct data structure. These operations are not o(1) so BitVector is not a true succinct data structure. However, it could potentially be extend to support this in the future.

Synopsis

# Documentation

data BitVector Source #

A little-endian bit vector of non-negative dimension.

Instances
 Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> BitVector -> c BitVector #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c BitVector #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c BitVector) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c BitVector) #gmapT :: (forall b. Data b => b -> b) -> BitVector -> BitVector #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> BitVector -> r #gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> BitVector -> r #gmapQ :: (forall d. Data d => d -> u) -> BitVector -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> BitVector -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> BitVector -> m BitVector #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> BitVector -> m BitVector #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> BitVector -> m BitVector # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian MethodsshowList :: [BitVector] -> ShowS # Source # Instance detailsDefined in Data.BitVector.LittleEndian Associated Typestype Rep BitVector :: Type -> Type # Methodsto :: Rep BitVector x -> BitVector # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodsstimes :: Integral b => b -> BitVector -> BitVector # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodsmconcat :: [BitVector] -> BitVector # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodsshrink :: BitVector -> [BitVector] # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodscoarbitrary :: BitVector -> Gen b -> Gen b # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodsbit :: Int -> BitVector #testBit :: BitVector -> Int -> Bool # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodsrnf :: BitVector -> () # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian MethodsofoldMap :: Monoid m => (Element BitVector -> m) -> BitVector -> m #ofoldr :: (Element BitVector -> b -> b) -> b -> BitVector -> b #ofoldl' :: (a -> Element BitVector -> a) -> a -> BitVector -> a #oall :: (Element BitVector -> Bool) -> BitVector -> Bool #oany :: (Element BitVector -> Bool) -> BitVector -> Bool #ocompareLength :: Integral i => BitVector -> i -> Ordering #otraverse_ :: Applicative f => (Element BitVector -> f b) -> BitVector -> f () #ofor_ :: Applicative f => BitVector -> (Element BitVector -> f b) -> f () #omapM_ :: Applicative m => (Element BitVector -> m ()) -> BitVector -> m () #oforM_ :: Applicative m => BitVector -> (Element BitVector -> m ()) -> m () #ofoldlM :: Monad m => (a -> Element BitVector -> m a) -> a -> BitVector -> m a #ofoldMap1Ex :: Semigroup m => (Element BitVector -> m) -> BitVector -> m # Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian Methodsotraverse :: Applicative f => (Element BitVector -> f (Element BitVector)) -> BitVector -> f BitVector #omapM :: Applicative m => (Element BitVector -> m (Element BitVector)) -> BitVector -> m BitVector # Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian MethodsofoldMapWithKey :: Monoid m => (MonoKey BitVector -> Element BitVector -> m) -> BitVector -> m #ofoldrWithKey :: (MonoKey BitVector -> Element BitVector -> a -> a) -> a -> BitVector -> a #ofoldlWithKey :: (a -> MonoKey BitVector -> Element BitVector -> a) -> a -> BitVector -> a # Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian MethodsotraverseWithKey :: Applicative f => (MonoKey BitVector -> Element BitVector -> f (Element BitVector)) -> BitVector -> f BitVector #omapWithKeyM :: Monad m => (MonoKey BitVector -> Element BitVector -> m (Element BitVector)) -> BitVector -> m BitVector # Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian Methods Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian MethodsshowbList :: [BitVector] -> Builder #showtList :: [BitVector] -> Text #showtlList :: [BitVector] -> Text # type Rep BitVector Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian type Rep BitVector = D1 (MetaData "BitVector" "Data.BitVector.LittleEndian" "bv-little-1.1.0-inplace" False) (C1 (MetaCons "BV" PrefixI True) (S1 (MetaSel (Just "dim") SourceUnpack SourceStrict DecidedStrict) (Rec0 Word) :*: S1 (MetaSel (Just "nat") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Natural))) type Element BitVector Source # Since: 0.1.0 Instance detailsDefined in Data.BitVector.LittleEndian type Element BitVector = Bool type MonoKey BitVector Source # Since: 1.0.0 Instance detailsDefined in Data.BitVector.LittleEndian type MonoKey BitVector = Word

# Bit-stream conversion

fromBits :: Foldable f => f Bool -> BitVector Source #

Create a bit vector from a little-endian list of bits.

The following will hold:

length . takeWhile not === countLeadingZeros . fromBits
length . takeWhile not . reverse === countTrailingZeros . fromBits

Time: $$\, \mathcal{O} \left( n \right)$$

Since: 0.1.0

#### Examples

Expand
>>> fromBits [True, False, False]
[3]1


toBits :: BitVector -> [Bool] Source #

Create a little-endian list of bits from a bit vector.

The following will hold:

length . takeWhile not . toBits === countLeadingZeros
length . takeWhile not . reverse . toBits === countTrailingZeros

Time: $$\, \mathcal{O} \left( n \right)$$

Since: 0.1.0

#### Examples

Expand
>>> toBits [4]11
[True, True, False, True]


# Numeric conversion

Arguments

 :: Integral v => Word dimension of bit vector -> v signed, little-endian integral value -> BitVector

Create a bit vector of non-negative dimension from an integral value.

The integral value will be treated as an signed number and the resulting bit vector will contain the two's complement bit representation of the number.

The integral value will be interpreted as little-endian so that the least significant bit of the integral value will be the value of the 0th index of the resulting bit vector and the most significant bit of the integral value will be at index dimension − 1.

Note that if the bit representation of the integral value exceeds the supplied dimension, then the most significant bits will be truncated in the resulting bit vector.

Time: $$\, \mathcal{O} \left( 1 \right)$$

Since: 0.1.0

#### Examples

Expand
>>> fromNumber 8 96
[8]96

>>> fromNumber 8 -96
[8]160

>>> fromNumber 6 96
[6]32


toSignedNumber :: Num a => BitVector -> a Source #

Two's complement value of a bit vector.

Time: $$\, \mathcal{O} \left( 1 \right)$$

Since: 0.1.0

#### Examples

Expand
>>> toSignedNumber [4]0
0

>>> toSignedNumber [4]3
3

>>> toSignedNumber [4]7
7

>>> toSignedNumber [4]8
-8

>>> toSignedNumber [4]12
-4

>>> toSignedNumber [4]15
-1


toUnsignedNumber :: Num a => BitVector -> a Source #

Unsigned value of a bit vector.

Time: $$\, \mathcal{O} \left( 1 \right)$$

Since: 0.1.0

#### Examples

Expand
>>> toSignedNumber [4]0
0

>>> toSignedNumber [4]3
3

>>> toSignedNumber [4]7
7

>>> toSignedNumber [4]8
8

>>> toSignedNumber [4]12
12

>>> toSignedNumber [4]15
15


# Queries

Get the dimension of a BitVector. Preferable to finiteBitSize as it returns a type which cannot represent a non-negative value and a BitVector must have a non-negative dimension.

Time: $$\, \mathcal{O} \left( 1 \right)$$

Since: 0.1.0

#### Examples

Expand
>>> dimension [2]3
2

>>> dimension [4]12
4


Determine if any bits are set in the BitVector. Faster than (0 ==) . popCount.

Time: $$\, \mathcal{O} \left( 1 \right)$$

Since: 0.1.0

#### Examples

Expand
>>> isZeroVector [2]3
False

>>> isZeroVector [4]0
True


subRange :: (Word, Word) -> BitVector -> BitVector Source #

Get the inclusive range of bits in BitVector as a new BitVector.

If either of the bounds of the subrange exceed the bit vector's dimension, the resulting subrange will append an infinite number of zeroes to the end of the bit vector in order to satisfy the subrange request.

Time: $$\, \mathcal{O} \left( 1 \right)$$

Since: 0.1.0

#### Examples

Expand
>>> subRange (0,2) [4]7
[3]7

>>> subRange (1, 3) [4]7
[3]3

>>> subRange (2, 4) [4]7
[3]1

>>> subRange (3, 5) [4]7
[3]0

>>> subRange (10, 20) [4]7
[10]0


# Rank / Select

Arguments

 :: BitVector -> Word $$k$$, the rank index -> Word Set bits within the rank index

Determine the number of set bits in the BitVector up to, but not including, index k.

To determine the number of unset bits in the BitVector, use k - rank bv k.

Uses "broadword programming." Efficient on small BitVectors (10^3).

Time: $$\, \mathcal{O} \left( \frac{n}{w} \right)$$, where $$w$$ is the number of bits in a Word.

Since: 1.1.0

#### Examples

Expand
>>> let bv = fromNumber 128 0 setBit 0 setBit 65

>>> rank bv   0  -- Count how many ones in the first 0 bits (always returns 0)
0

>>> rank bv   1  -- Count how many ones in the first 1 bits
1

>>> rank bv   2  -- Count how many ones in the first 2 bits
1

>>> rank bv  65  -- Count how many ones in the first 65 bits
1

>>> rank bv  66  -- Count how many ones in the first 66 bits
1

>>> rank bv 128  -- Count how many ones in all 128 bits
2

>>> rank bv 129  -- Out-of-bounds, fails gracefully
2


Arguments

 :: BitVector -> Word $$k$$, the select index -> Maybe Word index of the k-th set bit

Find the index of the k-th set bit in the BitVector.

To find the index of the k-th unset bit in the BitVector, use select (complement bv) k.

Uses "broadword programming." Efficient on small BitVectors (10^3).

Time: $$\, \mathcal{O} \left( \frac{n}{w} \right)$$, where $$w$$ is the number of bits in a Word.

Since: 1.1.0

#### Examples

Expand
>>> let bv = fromNumber 128 0 setBit 0 setBit 65

>>> select bv 0  -- Find the 0-indexed position of the first one bit
Just 0

>>> select bv 1  -- Find the 0-indexed position of the second one bit
Just 65

>>> select bv 2  -- There is no 3rd set bit, select fails
Nothing