This is the reason that support for changing rounding modes is so incredibly important for numerical reliability. One of the best ways to assess if your algorit

This is the reason that support for changing rounding modes is so incredibly important for numerical reliability. One of the best ways to assess if your algorithm is numerically stable is to try it in all the rounding modes. If all of the answers are similar, you're probably doing ok. If they're wildly different, you may be computing complete nonsense.