bitvec
Spaceefficient bit vectors
https://github.com/Bodigrim/bitvec
LTS Haskell 21.13:  1.1.5.0 
Stackage Nightly 20230925:  1.1.5.0 
Latest on Hackage:  1.1.5.0 
bitvec1.1.5.0@sha256:7c5639f95c8ce9d5be810152bfcaf701aac3b7d7f08685a869c7eda63dc2cd76,4734
Module documentation for 1.1.5.0
bitvec
A newtype over Bool
with a better Vector
instance: 8x less memory, up to 3500x faster.
The vector
package represents unboxed arrays of Bool
s
spending 1 byte (8 bits) per boolean.
This library provides a newtype wrapper Bit
and a custom instance
of an unboxed Vector
, which packs bits densely,
achieving an 8x smaller memory footprint.
The performance stays mostly the same;
the most significant degradation happens for random writes
(up to 10% slower).
On the other hand, for certain bulk bit operations
Vector Bit
is up to 3500x faster than Vector Bool
.
Thread safety
Data.Bit
is faster, but writes and flips are not threadsafe. This is because naive updates are not atomic: they read the whole word from memory, then modify a bit, then write the whole word back. Concurrently modifying nonintersecting slices of the same underlying array may also lead to unexpected results, since they can share a word in memory.Data.Bit.ThreadSafe
is slower (usually 1020%), but writes and flips are threadsafe. Additionally, concurrently modifying nonintersecting slices of the same underlying array works as expected. However, operations that affect multiple elements are not guaranteed to be atomic.
Quick start
Consider the following (very naive) implementation of
the sieve of Eratosthenes. It returns a vector with True
at prime indices and False
at composite indices.
import Control.Monad
import Control.Monad.ST
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as MU
eratosthenes :: U.Vector Bool
eratosthenes = runST $ do
let len = 100
sieve < MU.replicate len True
MU.write sieve 0 False
MU.write sieve 1 False
forM_ [2 .. floor (sqrt (fromIntegral len))] $ \p > do
isPrime < MU.read sieve p
when isPrime $
forM_ [2 * p, 3 * p .. len  1] $ \i >
MU.write sieve i False
U.unsafeFreeze sieve
We can switch from Bool
to Bit
just by adding newtype constructors:
import Data.Bit
import Control.Monad
import Control.Monad.ST
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as MU
eratosthenes :: U.Vector Bit
eratosthenes = runST $ do
let len = 100
sieve < MU.replicate len (Bit True)
MU.write sieve 0 (Bit False)
MU.write sieve 1 (Bit False)
forM_ [2 .. floor (sqrt (fromIntegral len))] $ \p > do
Bit isPrime < MU.read sieve p
when isPrime $
forM_ [2 * p, 3 * p .. len  1] $ \i >
MU.write sieve i (Bit False)
U.unsafeFreeze sieve
The Bit
based implementation requires 8x less memory to store
the vector. For large sizes it allows to crunch more data in RAM
without swapping. For smaller arrays it helps to fit into
CPU caches.
> listBits eratosthenes
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
There are several highlevel helpers, digesting bits in bulk,
which makes them up to 64x faster than the respective counterparts
for Vector Bool
. One can query the population count (popcount)
of a vector (giving us the primecounting function):
> countBits eratosthenes
25
And vice versa, query an address of the nth set bit (which corresponds to the nth prime number here):
> nthBitIndex (Bit True) 10 eratosthenes
Just 29
One may notice that the order of the inner traversal by i
does not matter and get tempted to run it in several parallel threads.
In this case it is vital to switch from Data.Bit
to Data.Bit.ThreadSafe
,
because the former is not threadsafe with regards to writes.
There is a moderate performance penalty (usually 1020%)
for using the threadsafe interface.
Sets
Bit vectors can be used as a blazingly fast representation of sets,
as long as their elements are Enum
eratable and sufficiently dense,
leaving IntSet
far behind.
For example, consider three possible representations of a set of Word16
:
 As an
IntSet
with a readily availableunion
function.  As a 64klong unboxed
Vector Bool
, implementing union aszipWith ()
.  As a 64klong unboxed
Vector Bit
, implementing union aszipBits (..)
.
When the simd
flag is enabled,
according to our benchmarks (see bench
folder),
the union of Vector Bit
evaluates magnitudes faster
than the union of nottoosparse IntSet
s
and stunningly outperforms Vector Bool
.
Here are benchmarks on MacBook M2:
union
16384
Vector Bit:
61.2 ns ± 3.2 ns
Vector Bool:
96.1 μs ± 4.5 μs, 1570.84x
IntSet:
2.15 μs ± 211 ns, 35.06x
32768
Vector Bit:
143 ns ± 7.4 ns
Vector Bool:
225 μs ± 16 μs, 1578.60x
IntSet:
4.34 μs ± 429 ns, 30.39x
65536
Vector Bit:
249 ns ± 18 ns
Vector Bool:
483 μs ± 28 μs, 1936.42x
IntSet:
8.77 μs ± 835 ns, 35.18x
131072
Vector Bit:
322 ns ± 30 ns
Vector Bool:
988 μs ± 53 μs, 3071.83x
IntSet:
17.6 μs ± 1.6 μs, 54.79x
262144
Vector Bit:
563 ns ± 27 ns
Vector Bool:
2.00 ms ± 112 μs, 3555.36x
IntSet:
36.8 μs ± 3.3 μs, 65.40x
Binary polynomials
Binary polynomials are polynomials with coefficients modulo 2.
Their applications include coding theory and cryptography.
While one can successfully implement them with the poly
package,
operating on UPoly Bit
,
this package provides even faster arithmetic routines
exposed via the F2Poly
data type and its instances.
> :set XBinaryLiterals
>  (1 + x) * (1 + x + x^2) = 1 + x^3 (mod 2)
> 0b11 * 0b111 :: F2Poly
F2Poly {unF2Poly = [1,0,0,1]}
Use fromInteger
/ toInteger
to convert binary polynomials
from Integer
to F2Poly
and back.
Package flags

Flag
simd
, enabled by default.Use a C SIMD implementation for the ultimate performance of
zipBits
,invertBits
andcountBits
.
Similar packages

array
is memoryefficient forBool
, but lacks a handyVector
interface and is not threadsafe.
Additional resources
Changes
1.1.5.0

Make
zipBits
unconditionally strict in its second bit vector argument (thanks to @treeowl). 
Add
simd
flag (enabled by default) to use a C SIMD implementation forzipBits
,invertBits
,countBits
,bitIndex
,nthBitIndex
,selectBits
,excludeBits
,reverseBits
(thanks to @konsumlamm). 
Decomission
libgmp
flag.
1.1.4.0
 Include
Data.Bit.Gmp
only iflibgmp
flag is set.  Tweak inlining pragmas to inline less aggressively.
1.1.3.0
 Fix malformed
signum
forF2Poly
.
1.1.2.0
 Fix
setBit
,clearBit
,complementBit
to preserve vector’s length.  Fix various issues on bigendian architectures.
 Fix Cabal 3.7+ incompatibility.
1.1.1.0
 Export
BitVec
andBitMVec
constructors.
1.1.0.0
 Fix a grave bug in
bitIndex
.  Remove
integergmp
flag.  Make
libgmp
flag disabled by default. Users are strongly encouraged to enable it whenever possible.  Add
mapBits
andmapInPlace
functions.  Add
cloneToByteString
andcloneFromByteString
functions.
1.0.3.0
 Add
Bits (Vector Bit)
instance.  Add
castFromWords8
,castToWords8
,cloneToWords8
to facilitate interoperation withByteString
.
1.0.2.0
 Fix outofbounds writes in mutable interface.
 Improve threadsafety of mutable interface.
 Add extended GCD for
F2Poly
.  Change
Show
instance ofF2Poly
.
1.0.1.2
 Fix more bugs in
F2Poly
multiplication.
1.0.1.1
 Fix bugs in
F2Poly
multiplication.  Performance improvements.
1.0.1.0
 Implement arithmetic of binary polynomials.
 Add
invertBits
andreverseBits
functions.  Add
Num
,Real
,Integral
,Fractional
andNFData
instances.  Performance improvements.
1.0.0.1
 Performance improvements.
1.0.0.0
 Redesign API from the scratch.
 Add a threadsafe implementation.
 Add
nthBitIndex
function.
0.2.0.1
 Fix
Read
instance.
0.2.0.0
 Remove handwritten
Num
,Real
,Integral
,Bits
instances.  Derive
Bits
andFiniteBits
instances.  Expose
Bit
constructor directly and removefromBool
function.  Rename
toBool
tounBit
.
0.1.1.0
 Fix bugs in
MVector
andVector
instances ofBit
.  Speed up
MVector
andVector
instances ofBit
.