On Sun, Jul 05, 2020 at 12:15:27PM -0400, David Mertz wrote:
> This is a digression, but does anyone have a nice example IN PYTHON of
> arriving at a NaN without going through infinity. I think Julia is right
> and Python is wrong about '0/0', but as things are, that's not an example.
I wouldn't expect one in Python, I think there is an unofficial policy
of ensuring that Python builtins and the math library will not return
NANs unless passed a NAN, or at least an INF, rather they will raise.
> > >>> 1e1000-1e1000
> > nan
is just a funny way of writing INF - INF :-)
The standard library *does* seem to have taken pains to avoid "finite nans." It kinda weakens your case about worrying about doing clamp() right in the face of NaNs :-).
I recognize there are funny ways of writing infinity. But since Python really doesn't quite follow IEEE-754 on 0/0, or math.fmod(x, 0.), or a few other places it might arise in "natural" operations (i.e. it's easy not to notice that your 'y' has become zero.
It also looks like the trig functions are pruned to those that don't have undefined values for numbers I can type in. I can *type* `math.tan(math.pi/2)`, of course. But math.pi is a little bit smaller than the actual pi, so I just get a big number for an answer. But I cannot try the hypothetical:
>>> math.cot(0)
nan
For what we actually have:
>>> math.tan(math.pi/2)
1.633123935319537e+16
One ULP more:
>> math.tan(np.nextafter(math.pi/2, np.inf))
-6218431163823738.0
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