I'm wondering why IEE754 standard defines two modes for processing tininess which finally assert the underflow flag.: before and after rounding.

From my understanding, the window for which tininess is different between the two modes is only 2⁻¹⁵⁰ wide, which is almost nothing. Considering implementation and PPA, I guess both modes do not make huge difference.

Moreover, we could imagine the same two modes for overflow flag processing, but the standard does not.

So what is the purpose of these two modes in the standard, what are their pros and cons?