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The standard library documentation for the math module states "All functions return a quiet NaN if at least one of the args is NaN." However, there are some exceptions to this rule, including:
math.pow(1.0, float('nan')) == 1.0
math.hypot(float('inf'), float('nan')) == float('inf')
abs(complex(float('nan'), float('inf'))) == float('inf')
The docs should be updated to reflect that such corner cases exist.

Thanks for reporting this.
Rather than documenting corner cases explicitly, maybe it would be enough to point to the C99 standard: the corner cases for the math functions should (modulo bugs) all follow Annex F of the C standard, while the corner cases for the cmath functions follow Annex G. This doesn't quite tell the complete story, because some functions (for example the cmath.rect function) don't appear in the C standards, but it would avoid cluttering the function descriptions with special cases.
Certainly the "All functions ..." sentence is inaccurate, and should be removed or revised. I believe it's true for all single-argument functions, though.

Hmm. Looking at the docs, there are a number of revisions that would be useful. For example, the docs mention signaling NaNs, but that doesn't make a lot of sense: Python essentially treats all NaNs as quiet. I'll add this to my to-do list.

Proposed update to math docs.

Looks good to me. Is it intentional that the paragraph about signaling NaNs is gone completely?
And is it intentional that you changed behavior -> behaviour? :)

Thanks, Georg.
Yes and No.
Yes: Perhaps I should say something about signaling nans, but what was there was just nonsense.
No: I'll drop the 'u' from behaviour, for the sake of consistency.

You don't need to :)

Too late! Committed in r79858 (trunk) through r79861 (release31-maint).
I added a couple of sentences about signaling nans.
Thanks for reviewing!

You didn't give me the chance to review the new sentences! Now I have to tell you that there is now "NaN", "*NaN*" and "nan" which looks inconsistent... :)

Rats.
nan->NaN in r79871 through r79874.
Then I reread your message...
*NaN* -> Nan in r79875 (trunk); will merge to other branches tomorrow when my brain might be working again.