Fastest popcount https://en.wikipedia.org/wiki/Hamming_weight

popcount.cc

#include <limits>
#include <climits>
#include <type_traits>

template <int bit>
struct fill_bits
{
	template <typename Int>
	static constexpr auto apply(Int n) -> Int
	{
		return _lambda(fill_bits<bit / 2>::apply(n));
	}

private:
	template <typename Int>
	static constexpr auto _lambda(Int x) -> Int
	{
		return (x << (bit / 2)) ^ x;
	}
};

template <>
struct fill_bits<CHAR_BIT>
{
	template <typename Int>
	static constexpr auto apply(Int n) -> Int
	{
		return n;
	}
};

template <typename Int>
constexpr auto magic(Int n)
	-> typename std::enable_if<std::is_unsigned<Int>::value, Int>::type
{
	return fill_bits<std::numeric_limits<Int>::digits>::apply(n);
}

template <typename Int>
struct m1 : std::integral_constant<Int, magic(Int(0x55))> {};

template <typename Int>
struct m2 : std::integral_constant<Int, magic(Int(0x33))> {};

template <typename Int>
struct m4 : std::integral_constant<Int, magic(Int(0x0f))> {};

template <typename Int>
struct h01 : std::integral_constant<Int, magic(Int(0x01))> {};

template <typename Int>
/* c++14 */ inline auto popcount(Int x) -> std::size_t
{
	x -= (x >> 1) & m1<Int>();
	x = (x & m2<Int>()) + ((x >> 2) & m2<Int>());
	x = (x + (x >> 4)) & m4<Int>();
	return Int(x * h01<Int>()) >>
	    (std::numeric_limits<Int>::digits - CHAR_BIT);
}

#include <iostream>
#include <chrono>
#include <cstdlib>

int main() {
	using namespace std::chrono;
	using traits =  std::numeric_limits<uint32_t>;

	steady_clock::time_point t1, t2;

	t1 = steady_clock::now();
	for (uint32_t x = 0; x < traits::max(); ++x)
		if (popcount(x) > traits::digits)
			std::exit(1);
	t2 = steady_clock::now();

	std::cout << "my popcount: "
	    << duration_cast<duration<double>>(t2 - t1).count() << std::endl;

	t1 = steady_clock::now();
	for (uint32_t x = 0; x < traits::max(); ++x)
		if (__builtin_popcount(x) > traits::digits)
			std::exit(1);
	t2 = steady_clock::now();

	std::cout << "__builtin_popcount: "
	    << duration_cast<duration<double>>(t2 - t1).count() << std::endl;
}