Without looking into the details, the problem might be that two n-bit numbers x and y might have continued fractions for sqrt(x) and sqrt(y) which differ very f

Without looking into the details, the problem might be that two n-bit numbers x and y might have continued fractions for sqrt(x) and sqrt(y) which differ very far along. Also, the continued fractions themselves can get more and more expensive to compute as you go along; possible exponentially more, but I'm not sure. Also, two continued fractions are not necessarily easy to compare. It's not a positional notation like decimal or binary.