bnd timecode: beat + numer/denom

bnd.cc

#include <stdexcept>
#include <iostream>
#include <chrono>
using std::cout;
using std::endl;

//         numer
// beat + ------- = beat (add) numer (over) denom -> band or bnd
//         denom

// must NOT reduce!
struct bnd
{
	using  beat_type = int;
	using numer_type = int;
	using denom_type = numer_type;

	 beat_type b = 0;
	numer_type n = 0;
	denom_type d = 1;

	bnd() = default;
	bnd(beat_type b_, numer_type n_, denom_type d_)
		: b{b_}, n{n_}, d{d_}
	{
		if (!d_) throw std::invalid_argument{"denominator cannot be zero."};
		b += n / d;
		n %= d;
	}

	explicit operator double() const { return b + double(n)/d; }
};

bool operator<(bnd const& a, bnd const& b)
{
	if (a.b < b.b) return true;
	if (a.b > b.b) return false;
	return (a.n*b.d < b.n*a.d);
}

template <class T>
decltype(auto) operator*(bnd const& time, T b)
{
	static_assert(std::is_integral<T>(),
			"a bnd can only be mutiplied by an integral.");
	return b*time.b + b*time.n / time.d;
}

bool operator==(bnd const& a, bnd const& b)
{
	return (a.b == b.b && a.n*b.d == b.n*a.d);
}

std::ostream& operator<<(std::ostream& o, bnd const& time)
{
	o << time.b << "+" << time.n << "/" << time.d;
	return o;
}

template <class Duration>
Duration bnd_to_time(bnd const& b, int bpm)
{
	using rep = typename Duration::rep;
	using period = typename Duration::period;
	return Duration((b * period::den) * 60 / period::num / bpm);
}

int main()
{
	bnd a{1, 8, 6};
	bnd b{1, 4, 3};
	cout << a << " == " << b << " -> " << (a == b) << endl;
	cout << a << " <  " << b << " -> " << (a <  b) << endl;
	cout << double(a) << endl;
	cout << double(b) << endl;
	cout << a*2 << endl;
	cout << a*3 << endl;
	cout << a*4 << endl;
	cout << a*5 << endl;
	cout << a*6 << endl;
	cout << a*10000 << endl;
	cout << double(a)*1.2 << endl;
	cout << a << "beat at 72bpm = "
		 << bnd_to_time<std::chrono::milliseconds>(a, 72).count()
		 << "ms" << endl;
};