Remove extra rounding mode changes for sqrt for interval

[sloriot]

The only place where the function is call is in Interval_nt::sqrt() and that functions start with the creation of a protector.
Even worse, if we are using interval with no protection, we get an incorrect rounding mode after a call to sqrt.

[mglisse]

Uh? I agree that it isn't optimal (there is already a comment saying so), it may even be wrong in the no-protection case as you mention, but completely removing the only place that sets the rounding mode to "down" cannot be right. For the lower bound, we need to call sqrt with the rounding mode set towards -inf or 0 (all other interval operations use +inf).

[sloriot]

Uh? I agree that it isn't optimal (there is already a comment saying so), it may even be wrong in the no-protection case as you mention, but completely removing the only place that sets the rounding mode to "down" cannot be right. For the lower bound, we need to call sqrt with the rounding mode set towards -inf or 0 (all other interval operations use +inf).

As stated above, the only function calling it has a protector here so it seems correct to me.

[mglisse]

As stated above, the only function calling it has a protector here so it seems correct to me.

That protector sets the rounding mode to UP, which is good for the upper bound, but not for the lower bound, which needs the rounding mode set to DOWN. For other operations, we use tricks (-(-a)+(-b) instead of a+b for instance) so we can emulate rounding DOWN using UP, but for sqrt I am not aware of any such trick, we really need to compute sup and inf using 2 different rounding modes.