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libpopcnt.h is a header-only C/C++ library for counting the number of 1 bits (bit population count) in an array as quickly as possible using specialized CPU instructions i.e. POPCNT, AVX2, AVX512, NEON. libpopcnt.h has been tested successfully using the GCC, Clang and MSVC compilers.

The algorithms used in libpopcnt.h are described in the paper Faster Population Counts using AVX2 Instructions by Daniel Lemire, Nathan Kurz and Wojciech Mula (23 Nov 2016).

How it works

On x86 CPUs libpopcnt.h uses a combination of 4 different bit population count algorithms:

  • For array sizes < 512 bytes a POPCNT algorithm is used.
  • For array sizes ≥ 512 bytes an AVX2 algorithm is used.
  • For array sizes ≥ 1024 bytes an AVX512 algorithm is used.
  • For CPUs without POPCNT instruction a portable integer algorithm is used.

Note that libpopcnt.h works on all CPUs, it checks at run-time whether your CPU supports POPCNT, AVX2, AVX512 before using it and it is also thread-safe.


#include "libpopcnt.h"

 * Count the number of 1 bits in the data array
 * @data: An array
 * @size: Size of data in bytes
uint64_t popcnt(const void* data, uint64_t size);


This benchmark shows the speedup of the 4 popcount algorithms used on x86 CPUs compared to the basic lookup-8 popcount algorithm for different array sizes (in bytes).

Algorithm 32 B 64 B 128 B 256 B 512 B 1024 B 2048 B 4096 B
lookup-8 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
bit-parallel-mul 1.41 1.54 1.63 1.78 1.60 1.62 1.63 1.64
builtin-popcnt 4.75 6.36 8.58 8.55 6.72 7.60 7.88 7.94
avx2-harley-seal 1.15 1.85 3.22 4.17 8.46 10.74 12.52 13.66
avx512-harley-seal 0.35 1.49 2.54 3.83 5.63 15.12 22.18 25.60

libpopcnt.h automatically picks the fastest algorithm for the given array size. This benchmark was run on an Intel Xeon Platinum 8168 CPU with GCC 5.4.

CPU architectures

libpopcnt.h has hardware accelerated popcount algorithms for the following CPU architectures:

x86 POPCNT, AVX2, AVX512
x86-64 POPCNT, AVX2, AVX512

For other CPU architectures a fast integer popcount algorithm is used.

How to compile

libpopcnt.h does not require any special compiler flags like -mavx2! In order to get the best performance we recommend however to compile with optimizations enabled e.g. -O3 or -O2.

cc  -O3 program.c
c++ -O3 program.cpp


cmake .
make -j
make test

The above commands also build the benchmark program which is useful for benchmarking libpopcnt.h. Below is a usage example run on an Intel Xeon Platinum 8168 CPU from 2017:

# Usage: ./benchmark [array bytes] [iters]
Iters: 10000000
Array size: 16.00 KB
Algorithm: AVX512
Status: 100%
Seconds: 1.59
103.4 GB/s


The vectorized popcount algorithms used in libpopcnt.h have originally been written by Wojciech Muła, I just made a convenient and portable C/C++ library using these algorithms.

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