General pow(xx,yy) function in Motion 10
Nate Hayes voted NO because of the inclusion of that function:
> The value of a general power function for floating-point seems clear
> to me, but I am a little skeptical of its value for interval computing.
> Mostly, the idea it returns bounds not of a single function but of a
> family of functions is a hard pill for me to swallow.
The general pow() function as proposed by Dan Zuras is not a conflation
of the family of rational-exponent functions -- though I agree that it
can be looked at this way, being defined by extending the concept of
completion-by-continuity to a set of values (in this case, two points
of equal magnitude but opposite signs). The real-positive function
with arbitrary-real exponent traditional pow() function then follows
naturally.
> If someone could provide practical examples of why it is required,
> I would change my vote to YES.
If the argument xx of pow(xx,yy) extends slightly into negative territory
due to earlier outward rounding, the result would also simply extend
slightly into negative territory, instead of having to raise an Undefined
decoration.
I do see an issue however in the case where yy is a singleton, because
that is now an exponent with an even denominator (in both decimal and
binary) if it has a non-zero fractional part. Dan's reasoning does not
apply to this case, and it would be necessary to raise "Undefined" if xx
contains negative points.
Whether that issue is a problem is a matter of perception.
Michel.
P.S. Perhaps we should push for a floating-point format with an odd base;
that would also eliminate all those annoying tie-break situations...
---Sent: 2009-12-05 19:08:37 UTC