What numerical algorithm is simplified by defining

Question

The IEEE 754 standard defines the square root of negative zero as negative zero. This choice is easy enough to rationalize, but other choices, such as defining sqrt(-0.0) as NaN, can be rationalized too and are easier to implement in hardware. If the fear was that programmers would write if (x >= 0.0) then sqrt(x) else 0.0 and be bitten by this expression evaluating to NaN when x is -0.0, then sqrt(-0.0) could have been defined as +0.0 (actually, for this particular expression, the results would be even more consistent).

Is there a numerical algorithm in particular where having sqrt(-0.0) defined as -0.0 simplifies the logic of the algorithm itself?

Answer 1

The only mathematically reasonable result is 0. There is a reasonable question of whether it should be +0 or -0. For most computations it makes no difference at all, but there are some specific complex expressions for which the result makes more sense under the -0 convention. The exact details are outside the scope of this site, but that's the gist of it.

I may explain some more when I'm not on vacation, if someone else doesn't beat me to it.