Mathematically, think of nan as 'indeterminate'. When you're trying to get the
magnitude of a vector, you know that it's infinite if even one of the
components is infinite. So, the fact that the other component is indeterminate
can be ignored. It's the same with math.pow(1.0, float('nan')); the second
argument simply doesn't matter when the first is 1.0.
FWIW, these conventions also exist in the C99 standard.
Hope this helps,
- David
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of
Steven D'Aprano
Sent: Tuesday, February 16, 2010 2:47 PM
To: [email protected]
Subject: Re: [Python-Dev] math.hypot, complex.__abs__, and documentation
On Wed, 17 Feb 2010 08:19:00 am David DiCato wrote:
> I have a minor concern about certain corner cases with math.hypot and
> complex.__abs__, namely when one component is infinite and one is not
> a number. If we execute the following code:
>
> import math
> inf = float('inf')
> nan = float('nan')
> print math.hypot(inf, nan)
> print abs(complex(nan, inf))
>
> ... then we see that 'inf' is printed in both cases. The standard
> library tests (for example, test_cmath.py:test_abs()) seem to test
> for this behavior as well, and FWIW, I personally agree with this
> convention.
What's the justification for that convention? It seems wrong to me.
If you expand out hypot and substitute a=inf and b=nan, you get:
>>> math.sqrt(inf*inf + nan*nan)
nan
which agrees with my pencil-and-paper calculation:
sqrt(inf*inf + nan*nan)
= sqrt(inf + nan)
= sqrt(nan)
= nan
--
Steven D'Aprano
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