On Mon, 2005-03-07 at 10:51 -0500, Robert Dewar wrote:
Paolo Carlini wrote:
Andrew Haley wrote:
F9.4.4 requires pow (x, 0) to return 1 for any x, even NaN.
Indeed. My point, basically, is that consistency appear to require the
very same behavior for *complex* zero^zero.
I am not sure, it looks like the standard is deliberately vague here,
and is not requiring this result.
Mathematically speaking zero^zero is undefined, so it should be NaN.
This already clear for real numbers: consider x^0 where x decreases
to zero. This is always 1, so you could deduce that 0^0 should be 1.
However, consider 0^x where x decreases to zero. This is always 0, so
you could deduce that 0^0 should be 0. In fact the limit of x^y
where x and y decrease to 0 does not exist, even if you exclude the
degenerate cases where x=0 or y=0. This is why there is no reasonable
mathematical value for 0^0.
Ciao,
Duncan.