> we've run the ball almost the full length of the field and then failed to put the ball over the goal line

But if we only go from "faithfully rounded" to "almost always correctly rounded", it seems to me that we're still a couple of millimetres away from that goal line. It wouldn't be hard to go for _always_ correctly rounded and actually get it over.

> Yes, the Emin and Emax for the default context is already almost big enough

I'm confused: big enough for what? I was thinking of the use-case where the inputs are all floats, in which case an Emax of 999 and an Emin of -999 would already be more than big enough.