[Bug math/14473] Inaccurate CPOWF function on x86_32 and x86_64

["joseph at codesourcery dot com" <sourceware-bugzilla at sourceware dot org>]

http://sourceware.org/bugzilla/show_bug.cgi?id=14473

--- Comment #1 from joseph at codesourcery dot com <joseph at codesourcery dot com> 2012-08-15 15:22:55 UTC ---
Again, please give testcases that use hex floats rather than using type 
punning, so that the test inputs can more readily be extracted for use 
elsewhere.

cpowf, cpow, cpowl are generically inaccurate for all architectures and 
floating-point formats - there's nothing x86-specific.  They are also by 
far the hardest complex functions to make accurate; the errors in this 
example are tiny compared to those you can get with properly chosen 
examples.  In general for long double you need to compute log and atan2 
results to over 16000 places to get good results for cpowl.  Consider 
cpowl (LDBL_MAX, I * LDBL_MAX) for example - you need to compute LDBL_MAX 
* log (LDBL_MAX), reduced mod 2pi.  Many cases will overflow or underflow 
but you still need to determine the signs of zero or infinity in those 
cases.

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