Barton–Nackman trick

Operators.cpp

template<typename T>
class Comparable
{
  friend bool operator!=(const T& x, const T& y) { return !(x == y); }
  friend bool operator>(const T& x, const T& y) { return y < x; }
  friend bool operator<=(const T& x, const T& y) { return !(y < x); }
  friend bool operator>=(const T& x, const T& y) { return !(x < y); }
};

template<typename T>
class Arithmetic
{
  friend T operator+(T x, const T& y) { return x += y; }
  friend T operator-(T x, const T& y) { return x -= y; }
  friend T operator*(T x, const T& y) { return x *= y; }
  friend T operator/(T x, const T& y) { return x /= y; }
  friend T operator%(T x, const T& y) { return x %= y; }

  friend T operator++(T x, int) { return ++x; }
  friend T operator--(T x, int) { return --x; }
};

template<typename T>
class Bitset
{
  friend T operator<<(T x, int shift) { return x <<= shift; }
  friend T operator>>(T x, int shift) { return x >>= shift; }

  friend T operator&(T x, const T& y) { return x &= y; }
  friend T operator|(T x, const T& y) { return x |= y; }
  friend T operator^(T x, const T& y) { return x ^= y; }
};