Binary Interpolative Coding

A C++ library implementing the Binary Interpolative Coding compression algorithm invented by Alistair Moffat and Lang Stuiver [1].

The algorithm can be used to compress sorted integer sequences (here, assumed to be increasing).

The implementation comes in different flavours: it can be specified the use of simple binary codes, left-most minimal codes and centered minimal codes. Additionally, the implementation is run-aware, i.e., it optimizes encoding/decoding of runs of consecutive identifiers.

All details and experiments are provided in the following technical report [2]

Table of contents

• Compiling the code
• Quick Start
• Encoding/decoding a collection of sequences
• Benchmark
• Author
• References

Compiling the code

The code is tested on Linux with gcc 7.3.0, 8.3.0, 9.2.1 and on Mac 10.14 with clang 10.0.0. To build the code, CMake is required.

Clone the repository with

git clone --recursive https://github.com/jermp/interpolative_coding.git

If you have cloned the repository without --recursive, you will need to perform the following commands before compiling:

git submodule init
git submodule update

To compile the code for a release environment and best performance (see file CMakeLists.txt for the used compilation flags), do:

mkdir build
cd build
cmake .. -DRUNAWARE=On
make

Hint: Use make -j4 to compile the library in parallel using, e.g., 4 jobs.

For a testing environment, use the following instead:

mkdir debug_build
cd debug_build
cmake .. -DCMAKE_BUILD_TYPE=Debug -DUSE_SANITIZERS=On
make

Quick Start

For a quick start, see the source file test/example.cpp. After compilation, run this example with

./example

A simpler variation is shown below.

#include <iostream>

#include "interpolative_coding.hpp"
using namespace bic;

template <typename BinaryCode>
void test(std::vector<uint32_t> const& in) {
    std::cout << "to be encoded:\n";
    for (auto x : in) {
        std::cout << x << " ";
    }
    std::cout << std::endl;

    uint32_t n = in.size();

    encoder<typename BinaryCode::writer> enc;
    enc.encode(in.data(), n);

    std::vector<uint32_t> out(n);
    decoder<typename BinaryCode::reader> dec;
    uint32_t m = dec.decode(enc.bits().data(), out.data());
    assert(m == n);

    std::cout << "decoded " << m << " values" << std::endl;
    std::cout << "total bits " << enc.num_bits() << std::endl;
    std::cout << static_cast<double>(enc.num_bits()) / m << " bits x key"
              << std::endl;

    std::cout << "decoded:\n";
    for (auto x : out) {
        std::cout << x << " ";
    }
    std::cout << std::endl;
}

int main(int argc, char** argv) {
    if (argc < 2) {
        std::cerr << argv[0] << " binary_code_type" << std::endl;
        return 1;
    }

    std::vector<uint32_t> in = {3, 4, 7, 13, 14, 15, 21, 25, 36, 38, 54, 62};

    std::string type(argv[1]);

    if (type == "binary") {
        test<binary>(in);
    } else if (type == "leftmost_minimal") {
        test<leftmost_minimal>(in);
    } else if (type == "centered_minimal") {
        test<centered_minimal>(in);
    } else {
        std::cerr << "unknown type '" << type << "'" << std::endl;
        return 1;
    }

    return 0;
}

Encoding/decoding a collection of sequences

Typically, we want to build all the sequences from a collection. In this case, we assume that the input collection is a binary file with all the sequences being written as 32-bit integers. In this library, we follow the input data format of the ds2i library: each sequence is prefixed by an additional 32-bit integer representing the size of the sequence. The collection file starts with a singleton sequence containing the universe of representation of the sequences, i.e., the maximum representable value.

We also assume all sequences are increasing.

The file data/test_collection.docs represents an example of such organization.

To encode all the sequences from this file, do:

./encode leftmost_minimal ../data/test_collection.docs -o test.bin

To decode all the sequences from the encoded file test.bin, do:

./decode leftmost_minimal test.bin

To check correctness of the implementation, use:

./check leftmost_minimal test.bin ../data/test_collection.docs

which will compare every decoded integer against the input collection.

Benchmark

For this benchmark we used the whole Gov2 datasets, containing 5,742,630,292 integers in 35,636,425 sequences.

We report the average number of bits per integer (bpi) and nanoseconds spent per decoded integer (with and without the run-aware optimization).

We used two different Intel processors: i7-7700 and i9-9900K, both clocked at 3.6 GHz and having 32K L1 caches for instructions and data. Both systems run Linux 4.4.0 and have 64 GB on RAM. The code was compiled with gcc 7.3.0 on the first system; with gcc 8.3.0 on the second. In both cases we used all optimizations (see also CMakeLists.txt).

Method	bpi	ns/int (run-aware) on i7-7700	ns/int (not run-aware) on i7-7700	ns/int (run-aware) on i9-9900K	ns/int (not run-aware) on i9-9900K
simple	3.532	3.45	4.65	2.52	3.37
left-most minimal	3.362	5.78	7.07	4.18	5.28
centered minimal	3.361	5.78	7.07	4.24	5.33

Author

• Giulio Ermanno Pibiri, giulio.ermanno.pibiri@isti.cnr.it

References

• [1] Alistair Moffat and Lang Stuiver. 2000. Binary Interpolative Coding for Effective Index Compression. Information Retrieval Journal 3, 1 (2000), 25 – 47.
• [2] Giulio Ermanno Pibiri. 2019. On Implementing the Binary Interpolative Coding Algorithm. Technical report. http://pages.di.unipi.it/pibiri/papers/BIC.pdf