Re: Table 4 proposal version 0.2...
Vincent
On 28 Mar 2012, at 11:59, Vincent Lefevre wrote:
> On 2012-03-23 10:57:20 -0700, Dan Zuras Intervals wrote:
>> The pow(x,y) = x^y (with the second parameter a floating-
>> point number) was defined as if it were the analytic
>> continuation of the x^n function into the Reals.
>
> No, it cannont be an analytic continuation, because the standard
> says:
>
> pow (x, ±0) is 1 for any x (even a zero, quiet NaN, or infinity)
>
> making pow not continuous at (0,0).
I just looked at what the standard says (IEEE 754-2008, §9.2.1) and am appalled.
I can just about live with max(x,NaN)=x, though there should have been two kinds of max & min defined, one of which does as above, and the other always propagates NaNs.
But the scenario
computation X produces x, but goes wrong so x is NaN,
computation Y produces y, which just by chance is exactly 0,
then we do x^y so the NaN disappears,
seems a HORRIBLE design choice.
Also pow(1,y) is always 1 even when y is a quiet NaN, and there are several other dodgy things like that.
Luckily I don't think it has any implications for how our interval functions are *defined*, though implementers should note it.
John Pryce