#include "Rational2.h"
#include <iostream>
#include <cstdlib>
using namespace std;

// gcd functions: would normally be a static members
int gcd2(int x, int y)
{
   return (y == 0) ? x : gcd2(y, x%y);
}

int gcd(int x, int y)
{
   // Force result to be positive
   return gcd2(abs(x), abs(y));
}

void Rational::reduce()
{
   int div = gcd(numerator, denominator);
   assert(div > 0);
   if (div != 1)
   {
      numerator /= div;
      denominator /= div;
   }
}

Rational& Rational::operator+=(const Rational& r)
{
   numerator = numerator*r.denominator + denominator*r.numerator;
   denominator = denominator*r.denominator;
   reduce();
   return *this;
}

Rational& Rational::operator-=(const Rational& r)
{
   numerator = numerator*r.denominator - denominator*r.numerator;
   denominator = denominator*r.denominator;
   reduce();
   return *this;
}

Rational& Rational::operator*=(const Rational& r)
{
   numerator *= r.numerator;
   denominator *= r.denominator;
   reduce();
   return *this;
}

Rational& Rational::operator/=(const Rational& r)
{
   assert(r.numerator != 0);
   numerator *= r.denominator;
   denominator *= r.numerator;
   reduce();
   return *this;
}

istream& operator>>(istream& is, Rational& r)
{
   char slash;
   is >> r.numerator >> slash;
   assert(slash == '/');
   is >> r.denominator;
   r.reduce();
   return is;
}

ostream& operator<<(ostream& os, const Rational& r)
{
   return os << r.numerator << '/' << r.denominator;
}