A fast Rational i c++, using Binary GCD ( __builtin_ctz )

Rational.h

#include <iostream>
#include <algorithm>

using namespace std;

class Rational {
private:
	size_t p;
	size_t q;
	
	size_t ctz(size_t x){
		return __builtin_ctz(x);
	}

	size_t gcd(size_t x, size_t y)
	{
		if (x == 0)
	    	return y;
	    if (y == 0)
			return x;
	    size_t cf2 = ctz(x | y);
	    x >>= ctz(x);
	    for (;;)
	    {
	        y >>= ctz(y);
	        if (x == y)
	            break;
	        if (x > y)
	            std::swap(x, y);
	        if (x == 1)
	            break;
	        y -= x;
	    }
	    return x << cf2;
	}

public:
	Rational(): p(0), q(1){};
	Rational(size_t a): p(a), q(1){};
	Rational(size_t p, size_t q): p(p), q(q) { 
		reduce();
	};

	friend ostream& operator<< (ostream& out, const Rational& r1);

	Rational operator+ (Rational& r) {
		return Rational(p * r.q + q * r.p, q * r.q);
	};

		Rational& operator+= (Rational& r){
			p = p * r.q + q * r.p;
			q = q * r.q;
			reduce();
			return *this;
		};

		void reduce() {
			if(q <= 1) return;
			size_t cd = gcd (p,q);
			if(cd > 1){
				p = p / cd;
				q = q / cd;
			}
		}

		
};
ostream& operator<< (ostream& out, const Rational& r)
{
	out << r.p;
	if(r.q > 1) out << "/" << r.q;
	return out;
}