[adgjlsfhk1]

this isn't true. floats don't have semantics of internals. they have semantics of exact points that do math with rounding (otherwise the result of subtracting 2 floats would sometimes be more than 1 float)

[throwawaymaths]

Moreover the spec defines rounding modes (rtnz, rtg, rtfz rtl) that are designed to exactly do interval arithmetic