#include <iostream>

class vec2d {
public:
    double x;
    double y;

    vec2d() : x(0), y(0) {
	std::cout << "default constructor." << std::endl;
    };

    vec2d(double a, double b) : x(a), y(b) {
	std::cout << "constructor with a=" << a << " b=" << b << std::endl;
    };

    vec2d(const vec2d & v) : x(v.x), y(v.y){
	std::cout << "copy constructor with v.x=" << v.x << " v.y=" << v.y << std::endl;
    };

    vec2d & operator = (/* *this is the default first operand */ const vec2d & v) {
	x = v.x;
	y = v.y;
	std::cout << "assignment operator with v.x=" << v.x << " v.y=" << v.y << std::endl;
	return *this;
    };	

    vec2d operator - (const vec2d & v2) {
	return vec2d(x - v2.x, y - v2.y);
    }

    operator int () {
	std::cout << "operator int." << std::endl;
	return 2;
    }
};

std::ostream & operator << (std::ostream & output, const vec2d & v) {
    output << "(" << v.x << "," << v.y << ")";
    return output;
}

vec2d operator - (const vec2d & v) {
    return vec2d(-v.x, -v.y);
}

vec2d operator - (const vec2d & v1, const vec2d & v2) {
    return vec2d(v1.x-v2.x, v1.y-v2.y);
}

int main() {
    vec2d v1; 			// invokes default constructor
    vec2d v2(10, 3.2); 		// invokes the second constructor
    vec2d v3 = v2; 		// invokes the copy constructor
    vec2d v4(v3); 		// also invokes the copy constructor

    v1 = -v4;
    std::cout << "v1 = " << v1 << std::endl;
    std::cout << "v4 = " << v4 << std::endl;
    double d = v1;
    std::cout << d << std::endl;
};

bool orthogonal(vec2d u, vec2d v) { // u and v are also copy-constructed
    return (u.x*v.x + u.y*v.y == 0);
}