A newtype wrapper with a custom instance of Data.Vector.Unboxed, which packs booleans as efficient as possible (8 values per byte). Vectors of Bit use 8x less memory than vectors of Bool (which stores one value per byte). but random writes are up to 10% slower.

Flip the bit at the given position. No bounds checks are performed. Equivalent to flip unsafeModify complement, but up to 2x faster.

In general there is no reason to unsafeModify bit vectors: either you modify it with id (which is id altogether) or with complement (which is unsafeFlipBit).

>>> Data.Vector.Unboxed.modify (\v -> unsafeFlipBit v 1) (read "[1,1,1]")
[1,0,1]

Flip the bit at the given position. Equivalent to flip modify complement, but up to 2x faster.

In general there is no reason to modify bit vectors: either you modify it with id (which is id altogether) or with complement (which is flipBit).

>>> Data.Vector.Unboxed.modify (\v -> flipBit v 1) (read "[1,1,1]")
[1,0,1]

Cast a vector of words to a vector of bits. Cf. castFromWordsM.

>>> castFromWords (Data.Vector.Unboxed.singleton 123)
[1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]

Try to cast a vector of bits to a vector of words. It succeeds if a vector of bits is aligned. Use cloneToWords otherwise. Cf. castToWordsM.

castToWords (castFromWords v) == Just v

Clone a vector of bits to a new unboxed vector of words. If the bits don't completely fill the words, the last word will be zero-padded. Cf. cloneToWordsM.

>>> cloneToWords (read "[1,1,0,1,1,1,1,0]")
[123]

Zip two vectors with the given function. Similar to zipWith, but up to 1000x (!) faster.

For sufficiently dense sets, represented as bitmaps, zipBits is up to 32x faster than union, intersection, etc.

>>> import Data.Bits
>>> zipBits (.&.) (read "[1,1,0]") (read "[0,1,1]") -- intersection
[0,1,0]
>>> zipBits (.|.) (read "[1,1,0]") (read "[0,1,1]") -- union
[1,1,1]
>>> zipBits (\x y -> x .&. complement y) (read "[1,1,0]") (read "[0,1,1]") -- difference
[1,0,0]
>>> zipBits xor (read "[1,1,0]") (read "[0,1,1]") -- symmetric difference
[1,0,1]

Invert (flip) all bits.

>>> invertBits (read "[0,1,0,1,0]")
[1,0,1,0,1]

Reverse the order of bits.

>>> reverseBits (read "[1,1,0,1,0]")
[0,1,0,1,1]

Return the index of the first bit in the vector with the specified value, if any. Similar to elemIndex, but up to 64x faster.

>>> bitIndex (Bit True) (read "[0,0,1,0,1]")
Just 2
>>> bitIndex (Bit True) (read "[0,0,0,0,0]")
Nothing

bitIndex bit == nthBitIndex bit 1

One can also use it to reduce a vector with disjunction or conjunction:

>>> import Data.Maybe
>>> isAnyBitSet   = isJust    . bitIndex (Bit True)
>>> areAllBitsSet = isNothing . bitIndex (Bit False)

Return the index of the n-th bit in the vector with the specified value, if any. Here n is 1-based and the index is 0-based. Non-positive n results in an error.

>>> nthBitIndex (Bit True) 2 (read "[0,1,0,1,1,1,0]")
Just 3
>>> nthBitIndex (Bit True) 5 (read "[0,1,0,1,1,1,0]")
Nothing

One can use nthBitIndex to implement to implement select{0,1} queries for succinct dictionaries.

Return the number of set bits in a vector (population count, popcount).

>>> countBits (read "[1,1,0,1,0,1]")
4

One can combine countBits with take to implement rank{0,1} queries for succinct dictionaries.

Return the indices of set bits in a vector.

>>> listBits (read "[1,1,0,1,0,1]")
[0,1,3,5]

For each set bit of the first argument, deposit the corresponding bit of the second argument to the result. Similar to the parallel deposit instruction (PDEP).

>>> selectBits (read "[0,1,0,1,1]") (read "[1,1,0,0,1]")
[1,0,1]

Here is a reference (but slow) implementation:

import qualified Data.Vector.Unboxed as U
selectBits mask ws == U.map snd (U.filter (unBit . fst) (U.zip mask ws))

For each unset bit of the first argument, deposit the corresponding bit of the second argument to the result.

>>> excludeBits (read "[0,1,0,1,1]") (read "[1,1,0,0,1]")
[1,0]

Here is a reference (but slow) implementation:

import qualified Data.Vector.Unboxed as U
excludeBits mask ws == U.map snd (U.filter (not . unBit . fst) (U.zip mask ws))

Cast a vector of words to a vector of bits. Cf. castFromWords.

Try to cast a vector of bits to a vector of words. It succeeds if a vector of bits is aligned. Use cloneToWordsM otherwise. Cf. castToWords.

Clone a vector of bits to a new unboxed vector of words. If the bits don't completely fill the words, the last word will be zero-padded. Cf. cloneToWords.

Zip two vectors with the given function. rewriting contents of the second argument. Cf. zipBits.

>>> import Data.Bits
>>> modify (zipInPlace (.&.) (read "[1,1,0]")) (read "[0,1,1]")
[0,1,0]

Warning: if the immutable vector is shorter than the mutable one, it is a caller's responsibility to trim the result:

>>> import Data.Bits
>>> modify (zipInPlace (.&.) (read "[1,1,0]")) (read "[0,1,1,1,1,1]")
[0,1,0,1,1,1] -- note trailing garbage

Invert (flip) all bits in-place.

>>> Data.Vector.Unboxed.modify invertInPlace (read "[0,1,0,1,0]")
[1,0,1,0,1]

Reverse the order of bits in-place.

>>> Data.Vector.Unboxed.modify reverseInPlace (read "[1,1,0,1,0]")
[0,1,0,1,1]

Same as selectBits, but deposit selected bits in-place. Returns a number of selected bits. It is caller's resposibility to trim the result to this number.

Same as excludeBits, but deposit excluded bits in-place. Returns a number of excluded bits. It is caller's resposibility to trim the result to this number.

Binary polynomials of one variable, backed by an unboxed Vector Bit.

Polynomials are stored normalized, without leading zero coefficients.

Ord instance does not make much sense mathematically, it is defined only for the sake of Set, Map, etc.

>>> :set -XBinaryLiterals
>>> -- (1 + x) (1 + x + x^2) = 1 + x^3 (mod 2)
>>> 0b11 * 0b111 :: F2Poly
F2Poly {unF2Poly = [1,0,0,1]}

Convert F2Poly to a vector of coefficients (first element corresponds to a constant term).

Make F2Poly from a list of coefficients (first element corresponds to a constant term).