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Bitvector

Concept

The concept fmindex_collection::Bitvector_c models a bitvector with rank support. Classes fulfilling this concept are guaranteed to provide following functionality:

Functionality Description
class is std::default_initializable<T>
class is std::movable<T>
T(size_t length, Proj proj)
auto size() const -> size_t Returns the number of bits of this vector.
auto symbol(size_t idx) const -> bool Returns the bit at position idx. Parameter must be 0 ≤ idx < size().
auto rank(size_t idx) const -> bool Returns the number of ones in the first idx bits. Parameter must be 0 ≤ idx ≤ size().

Examples usages

Creating a bitvector of length 100, in which every second bit is set to one. 

auto bitvector = T{100, [](size_t idx) {
    return idx % 2 == 0;
});

// prints the number of bits
std::cout << bitvector.size() << '\n';

// prints value of the 51th bit
std::cout << bitvector.symbol(50) << '\n';

// prints how many ones there are in the first 50bit
std::cout << bitvector.rank(50) << '\n';

Creating a bitvector of length 100, where bits 0-49 are set to 1 and then move it around. 

auto bitvector = T{100, [](size_t idx) {
    return idx < 50;
});

T bitvector2 = std::move(bitvector);

Implementations - Description

  • fmindex_collection::bitvector::Bitvector

    Consist of 3 independent arrays. 64bit values for bits, 8bit for blocks and 64bit for superblocks. Every 64bits a new block is started. Every 256bits a new superblock starts.

  • fmindex_collection::bitvector::CompactBitvector

    Consist of 3 interleaved arrays. Each DataBlock is 512 bits, and covers 6·64bits, each block is 9 bit and starts every 64bit, superblocks start ever 352 bits, 10bits are wasted for padding.

  • fmindex_collection::bitvector::CompactBitvector4Blocks

    Consist of 3 interleaved arrays. Each DataBlock is 352 bits, and covers 4·64bits, each block is 8 bit and starts every 64bit, superblocks start every 256 bits.

  • fmindex_collection::bitvector::SparseBLEBitvector

    Sparse Block Length Encoded Bitvector. !TODO add paper reference

Statistics

Memory

Percentage refer to how many ones where present in the input data.

Name 50% 25% 10% 5% 0.5%
Bitvector 1.38 1.38 1.38 1.38 1.38
CompactBitvector 1.33 1.33 1.33 1.33 1.33
CompactBitvector4Blocks 1.50 1.50 1.50 1.50 1.50
SparseBLEBitvector 2 1.72 1.29 0.95 0.82 0.70
SparseBLEBitvector 4 1.63 1.28 0.82 0.60 0.37
SparseBLEBitvector 8 1.54 1.41 0.96 0.63 0.23
SparseBLEBitvector 16 1.46 1.45 1.21 0.86 0.19
SparseBLEBitvector 32 1.42 1.42 1.37 1.15 0.25
SparseBLEBitvector 2/2 2.02 1.42 0.84 0.61 0.37
SparseBLEBitvector 4/2 1.80 1.42 0.84 0.54 0.21
SparseBLEBitvector 4/4 1.72 1.37 0.84 0.53 0.14
SparseBLEBitvector 8/2 1.63 1.49 1.01 0.65 0.15
SparseBLEBitvector 8/4 1.58 1.45 0.99 0.64 0.12
SparseBLEBitvector 8/8 1.56 1.43 0.98 0.65 0.12
SparseBLEBitvector 4/-2 2.02 1.42 0.84 0.61 0.37
SparseBLEBitvector 8/-2 1.89 1.39 0.82 0.54 0.21
SparseBLEBitvector 8/-4 1.80 1.42 0.84 0.54 0.21

Run-time

Input data was 100'000'000 bits with 50% of them ones.

Name Construct symbol() rank()
Bitvector 1.97ns 15.64ns 40.93ns
CompactBitvector 1.98ns 40.51ns 90.74ns
CompactBitvector4Blocks 2.39ns 28.72ns 47.80ns
SparseBLEBitvector 4 4.14ns 27.86ns 183.78ns
SparseBLEBitvector !4 3.58ns 40.56ns 56.90ns
SparseBLEBitvector 8/4 4.01ns 45.92ns 78.69ns
SparseBLEBitvector 8/-4 5.18ns 43.57ns 117.80ns

bit vector memory layout