On the subject of the floating-point math in general, I wonder what's the practical way to treat the extreme order values (close to zero ~ 1E-200, or infinity ~ 1E200, but not zero or inf)? This can take place in some iterative methods, expansion series, or around some singularities.<p>How reliable is it to keep the exreme orders in expectation that the resp. quatities would cancel the orders properly yielding a meaningful value (rounding wise)?<p>For example, calculating some resulting value function, expressed as<p>v(x)=f(x)/g(x),<p>where both f(x) and g(x) are oscillating with a number of roots in a given interval of x.