__builtin_cpow((0,0),(0,0))

[Ronny Peine]

Well, i'm studying mathematics and as i know so far 0^0 is always 1 (for 
real and complex numbers) and well defined even in numerical and 
theoretical mathematics. Could you point me to some publications which 
say other things?

cu, Ronny


Duncan Sands wrote:
> 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.
> 
>