[C++] Rust's BitIter in C++

bititer.hpp

// Inspired by https://lib.rs/crates/bit-iter

#include <algorithm>
#include <bitset>
#include <concepts>
#include <limits>

template <typename T>
requires std::unsigned_integral<T> class BitIter {
public:
	static constexpr auto BITS_IN_T = std::numeric_limits<T>::digits;
	static constexpr auto END_POS = BITS_IN_T + 1;

	class iterator {
	private:
		T value = {};
		unsigned int position = 0U;

	public:
		explicit iterator(T v, unsigned int p) : value{v}, position{p} {
		}

		bool operator==(const iterator&) const = default;

		iterator& operator++() {
			const auto bs = std::bitset<BITS_IN_T>{value};

			do {
				position += 1;
			} while (position < END_POS and bs[position] == false);

			return *this;
		}

		unsigned int operator*() const {
			return position;
		}
	};

	explicit BitIter(T t) : value{t} {
	}

	iterator begin() const {
		unsigned int position = 0U;
		const auto bs = std::bitset<BITS_IN_T>{value};
		while (position < END_POS and bs[position] == false) {
			position += 1;
		}
		return iterator{value, position};
	}

	iterator end() const {
		return iterator{value, END_POS};
	}

	T value;
};

main.cpp

#include "bititer.hpp"

#include <format>
#include <iostream>

template <typename T>
std::ostream& operator<<(std::ostream& os, const BitIter<T>& iter) {
	os << std::format("BitIter {{ value={}=0b{:b}, positions=", iter.value, iter.value);

	for (const auto pos : iter) {
		os << pos << ' ';
	}

	os << '}';
	return os;
}

int main() {
	for (auto i = 0U; i < 5; ++i) {
		const auto bi = BitIter{i};
		std::cout << bi << '\n';
	}
}