//  Fraction (Rational number) class implementation (see Fraction.hpp)
//  -----------------------------------------------     

#include "Fraction.hpp"
  
 long Fraction::gcd (LONG  m,  LONG  n) //  Greatest common divisor
 {return m % n ?  gcd(n, m % n) : n; }  //  (Recursive implementation)

 long Fraction::lcm(LONG m, LONG n)
 {return (m/gcd(m,n)) * n;}

 void Fraction::reduce()             //  Increase speed by nullifying or
 {long d = gcd(abs(numer),denom);    //   selectively executing this function,  
  numer /= d; denom /= d;            //    at increased risk of overflow.
 }

  Fraction& Fraction::operator+=(FRACTION rs) 
   {long d = lcm(denom, rs.denom);   //  Common divisor
    numer *= d / denom; denom = d;
    numer += (d / rs.denom) * rs.numer;
    reduce();
    return *this;
   }  

  Fraction& Fraction::operator-=(FRACTION rs) 
   {long d = lcm(denom, rs.denom);   //  Common divisor
    numer *= d / denom; denom = d;
    numer -= (d / rs.denom) * rs.numer;
    reduce();
    return *this;
   }  

  Fraction& Fraction::operator*=(FRACTION rs) 
   {numer *= rs.numer; denom *= rs.denom;
    reduce();   
    return *this;
   }  

  Fraction& Fraction::operator/=(FRACTION rs) 
   {numer *= rs.denom; denom *= rs.numer;
    reduce();
    return *this;
   }  


ostream& operator<<(ostream& s, FRACTION x)
    {return s << x.numerator() << '/' << x.denominator();}