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Compressed bitset in C++

What is this?

The class EWAHBoolArray is a compressed bitset data structure. It supports several word sizes by a template parameter (16-bit, 32-bit, 64-bit). You should expect the 64-bit word-size to provide better performance, but higher memory usage, while a 32-bit word-size might compress a bit better, at the expense of some performance.

The library also provides a basic BoolArray class which can serve as a traditional bitmap.

Real-world usage

EWAH is used to accelerate the distributed version control system Git.

The Java counterpart of this library (JavaEWAH) is part of Apache Hive and its derivatives (e.g., Apache Spark) and Eclipse JGit. It has been used in production systems for many years. It is part of major Linux distributions.

This library is used by database and information retrieval engines such as Hustle -- A column oriented, embarrassingly distributed relational event database. We find it in the fuzzing tool VUzzer.

When should you use a bitmap?

Sets are a fundamental abstraction in software. They can be implemented in various ways, as hash sets, as trees, and so forth. In databases and search engines, sets are often an integral part of indexes. For example, we may need to maintain a set of all documents or rows (represented by numerical identifier) that satisfy some property. Besides adding or removing elements from the set, we need fast functions to compute the intersection, the union, the difference between sets, and so on.

To implement a set of integers, a particularly appealing strategy is the bitmap (also called bitset or bit vector). Using n bits, we can represent any set made of the integers from the range [0,n): it suffices to set the ith bit is set to one if integer i is present in the set. Commodity processors use words of W=32 or W=64 bits. By combining many such words, we can support large values of n. Intersections, unions and differences can then be implemented as bitwise AND, OR and ANDNOT operations. More complicated set functions can also be implemented as bitwise operations.

When the bitset approach is applicable, it can be orders of magnitude faster than other possible implementation of a set (e.g., as a hash set) while using several times less memory.

When should you use compressed bitmaps?

An uncompressed BitSet can use a lot of memory. For example, if you take a BitSet and set the bit at position 1,000,000 to true and you have just over 100kB. That's over 100kB to store the position of one bit. This is wasteful even if you do not care about memory: suppose that you need to compute the intersection between this BitSet and another one that has a bit at position 1,000,001 to true, then you need to go through all these zeroes, whether you like it or not. That can become very wasteful.

This being said, there are definitively cases where attempting to use compressed bitmaps is wasteful. For example, if you have a small universe size. E.g., your bitmaps represent sets of integers from [0,n) where n is small (e.g., n=64 or n=128). If you can use an BitSet and it does not blow up your memory usage, then compressed bitmaps are probably not useful to you. In fact, if you do not need compression, then a BitSet offers remarkable speed. One of the downsides of a compressed bitmap like those provided by EWAHBoolArray is slower random access: checking whether a bit is set to true in a compressed bitmap takes longer.

How does EWAH compares with the alternatives?

EWAH is part of a larger family of compressed bitmaps that are run-length-encoded bitmaps. They identify long runs of 1s or 0s and they represent them with a marker word. If you have a local mix of 1s and 0, you use an uncompressed word.

There are many formats in this family beside EWAH:

  • Oracle's BBC is an obsolete format at this point: though it may provide good compression, it is likely much slower than more recent alternatives due to excessive branching.
  • WAH is a patented variation on BBC that provides better performance.
  • Concise is a variation on the patented WAH. It some specific instances, it can compress much better than WAH (up to 2x better), but it is generally slower.
  • EWAH is both free of patent, and it is faster than all the above. On the downside, it does not compress quite as well. It is faster because it allows some form of "skipping" over uncompressed words. So though none of these formats are great at random access, EWAH is better than the alternatives.

There are other alternatives however. For example, the Roaring format is not a run-length-encoded hybrid. It provides faster random access than even EWAH.


Apache License 2.0.

Update (May 20th, 2013): though by default I use the Apache License 2.0 (which is compatible with GPL 3.0), you can also consider this library licensed under GPL 2.0.


None. (Will work under MacOS, Windows or Linux.)

Compilers tested: clang++, g++, Intel compiler, Microsoft Visual Studio

It works on x64 processors as well as on 32-bit ARM processors.

Versions 0.5 and above assume that the compiler supports the C++11 standard.

Usage (Linux and Linux-like systems)

cmake -B build 
cmake --build build
cd build

Usage (Visual Studio under Windows)

To build with at least Visual Studio 2017 directly in the IDE:

  • Grab the code from GitHub, e.g., by cloning it using GitHub Desktop.
  • Select the Visual C++ tools for CMake optional component when installing the C++ Development Workload within Visual Studio.
  • Within Visual Studio use File > Open > Folder... to open the CRoaring folder.
  • Right click on CMakeLists.txt in the parent directory within Solution Explorer and select Build to build the project.
  • For testing, in the Standard toolbar, drop the Select Startup Item... menu and choose one of the tests. Run the test by pressing the button to the left of the dropdown.

Quick code sample

  #include "ewah.h"
  using namespace ewah;

  typedef EWAHBoolArray<uint32_t> bitmap;

  bitmap bitset1 =
      bitmap::bitmapOf(9, 1, 2, 1000, 1001, 1002, 1003, 1007, 1009, 100000);
  std::cout << "first bitset : " << bitset1 << std::endl;
  bitmap bitset2 = bitmap::bitmapOf(5, 1, 3, 1000, 1007, 100000);
  std::cout << "second bitset : " << bitset2 << std::endl;
  bitmap bitset3 = bitmap::bitmapOf(3, 10, 11, 12);
  std::cout << "third  bitset : " << bitset3 << std::endl;
  bitmap orbitset = bitset1 | bitset2;
  bitmap andbitset = bitset1 & bitset2;
  bitmap xorbitset = bitset1 ^ bitset2;
  bitmap andnotbitset = bitset1 - bitset2;


Please see examples/example.cpp. For an example with tabular data, please see example2.cpp.

Further reading

Please see

  • Daniel Lemire, Owen Kaser, Nathan Kurz, Luca Deri, Chris O'Hara, François Saint-Jacques, Gregory Ssi-Yan-Kai, Roaring Bitmaps: Implementation of an Optimized Software Library, Software: Practice and Experience 48 (4), 2018 arXiv:1709.07821
  • Daniel Lemire, Owen Kaser, Kamel Aouiche, Sorting improves word-aligned bitmap indexes. Data & Knowledge Engineering 69 (1), pages 3-28, 2010.
  • Owen Kaser and Daniel Lemire, Compressed bitmap indexes: beyond unions and intersections, Software: Practice and Experience 46 (2), 2016.

Node/JavaScript wrapper

Dimitrios Vasilas wrote a wrapper for JavaScript.

You can install it by typing:

    npm install -g node-gyp
    npm install node-bitmap-ewah

Ruby wrapper

Josh Ferguson wrote a wrapper for Ruby. The implementation is packaged and installable as a ruby gem.

You can install it by typing:

    gem install ewah-bitset

Persistent storage

We do not correct for the endianess. If you use both little endian and big endian machines, you should be careful. Thankfully, big endian hardware is vanishingly rare.