inline doubledouble operator +(const doubledouble& x, const doubledouble& y) {
  double H, h, T, t, S, s, e, f;

  S = x.hi + y.hi; 
  T = x.lo + y.lo; 
  e = S - x.hi; 
  f = T - x.lo; 
  s = S - e; 
  t = T - f; 
  s = ( y.hi - e ) + ( x.hi - s); 
  t = ( y.lo - f ) + ( x.lo - t ); 
  e = s + T; 
  H = S + e; 
  h = e + ( S - H ); 
  e = t + h;

  doubledouble z; 
  z.hi = H + e; 
  z.lo = e + double( H - z.hi ); 

  return z;
}