Interval enclosure of X**Y for negative x in X

[David G Hough at validgh]

> In a context where no full complex interval arithmetic is provided,
> there is no point at all in thinking of function as restrictions of
> complex-valued functions.

I remember in beginning calculus being told that many of the odd things
we were told would only make sense when we studied complex analytic function
theory, and indeed as I discovered some years later in graduate school, 
that was true!    So I still tend to take the complex point of view when
trying to understand even real analytic functions.   It's not the right
point of view for all applications but seems to correspond to a lot of
computational physics and chemistry.

A definition of "exceptional situation" is "a situation where no matter what
you do, somebody will take exception" and this case is one of them, although
perhaps simpler than the issues around interval 0**0, a topic for another
time.

> Perhaps Dr. Hough could expand on the practical disadvantage of 
> giving X**Y more useful values in case X contains negative numbers.

It's a question of error detection.   Typical physics codes exploit
x**y (as opposed to x**n) with expressions like z**0.62
where the 0.62 appears to be an empirical constant (or more complicated
expression) and is not intended to
represent some fraction, so any negative argument z would be an error.
Certainly the philosophy of IEEE 754 leans often toward simplifying expert
programming rather than maximizing error detection, but there's a limit
to how far one wants to go in that direction, and in this case the issue
is easily resolved by defining a new function that does exactly what's wanted
here.    There's no absolute criterion to apply here, just judgments about
the needs of various programmers who may be writing expert interval
programs or inexpertly converting point programs to intervals.