[Bug math/13932] x86_64 pow unexpectedly slow for some inputs

["siddhesh at redhat dot com" <sourceware-bugzilla@sourceware.org>]

http://sourceware.org/bugzilla/show_bug.cgi?id=13932

--- Comment #8 from Siddhesh Poyarekar <siddhesh at redhat dot com> 2013-03-11 10:19:19 UTC ---
(In reply to comment #7)
> Hi, thanks for your work. Personally, I would be interested to have a pow
> version that is perhaps less precise but that does not have  such nasty
> corner-cases. A 4x improvement is nice, but given that the worst-case may be
> 12,000x slower, it is not a definitive solution.
> 
> There are some implementations on the net that perhaps could be used when
> -ffast-math is given?
> 
> http://jrfonseca.blogspot.be/2008/09/fast-sse2-pow-tables-or-polynomials.html
> 
> http://www.dctsystems.co.uk/Software/power.html
> 
> http://martin.ankerl.com/2012/01/25/optimized-approximative-pow-in-c-and-cpp/
> 
> I am no expert in IEEE floating-point arithmetic, so it may well be that those
> implementations produce extremely bad approximations for some inputs. Is that
> the case?

They're all in a way subsets of what the fast phase of libm does, so we don't
really need to reimplement libm to take advantage of those ideas.

That said, there is indeed a strong case for fast and (for some inputs)
imprecise computations of transcendentals.  That probably won't be the default
in glibc, but I won't rule out the possibility of having an alternate library
or configuration, provided there is consensus in the glibc community for it.

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