Why does NaN^0 == 1

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This is referenced in the help page referenced by ?'NaN'

“The IEC 60559 standard, also known as the ANSI/IEEE 754 Floating-Point Standard.

http://en.wikipedia.org/wiki/NaN.”

And there you find this statement regarding what should create a NaN:

 "There are three kinds of operations that can return NaN:[5]
       Operations with a NaN as at least one operand.

It is probably is from the particular C compiler, as signified by the Note you referenced. This is what the GNU C documentation says:

http://www.gnu.org/software/libc/manual/html_node/Infinity-and-NaN.html

” NaN, on the other hand, infects any calculation that involves it. Unless the calculation would produce the same result no matter what real value replaced NaN, the result is NaN.”

So it seems that the GNU-C people have a different standard in mind when writing their code. And the 2008 version of ANSI/IEEE 754 Floating-Point Standard is reported to make that suggestion:

http://en.wikipedia.org/wiki/NaN#Function_definition

The published standard is not free. So if you are have access rights or money you can look here:

http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4610933

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