[Bug math/14412] Removal of sysdeps/x86_64/fpu/s_sincos.S causes regressions

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

http://sourceware.org/bugzilla/show_bug.cgi?id=14412

--- Comment #45 from Siddhesh Poyarekar <siddhesh at redhat dot com> 2013-04-30 05:41:27 UTC ---
(In reply to comment #32)
> I suspect this is just a boundary issue (the [] should be () in the range)
> since slightly smaller values give more reasonable, but still badly wrong,
> results. For example if x is 0x1p62,

Yes, it is () and not [], according to the manual.

> 
> -0.702922443619209 -0.707132927452779
> 
> which is wrong in the third decimal place.
> 

This is not restricted to numbers on the boundary.  A quick google search on
accuracy of fsincos will show that there are numbers even close to pi/2 that
are way off in terms of accuracy.

> Siddhesh, could you explain the motivation for "overloading" the meaning of
> "_finite" with "fast but wrong"? I'm guessing the idea is that you're thinking
> finite math implies not just lack of infinities but also "unreasonably large"
> inputs? This is definitely the glibc team's call, since there's no reasonable
> basis for assuming you'll get correct results from non-default
> performance-oriented math settings, but I think some justification would be
> nice.

That was a mistake - I somehow muddled it up with -ffast-math in my head.

I'm going to first try to see if the default sincos can be made faster.  Jakub
pointed out offline that the argument reduction code is duplicated in the calls
to __sin and __cos and consolidating that in sincos should definitely be a good
first step.

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