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

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

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

--- Comment #23 from joseph at codesourcery dot com <joseph at codesourcery dot com> 2013-04-26 15:07:02 UTC ---
It's only a limited subset of transcendental functions for which glibc is 
trying to be correctly rounding, and only for double for those functions; 
for most functions the aim is generally errors within "a few" ulps (and 
ISO C doesn't specify particular accuracy requirements), though correctly 
rounding would be some sort of ideal.

Implementing the proposed TS 18661 bindings to IEEE 754-2008 would be a 
huge amount of work (and require compiler work as well), but if anyone 
gets the time for that work then I believe part 4 of the draft TS will 
reserve names such as crsin for correctly rounding functions (and 
crsinf128 for correctly rounding sine for _Float128, etc.), without 
requiring those functions, so it might make sense eventually to provide 
those names for correctly-rounding functions where available without 
making them the default versions.  So far I'm still working on going 
through the accumulated libm bugs that don't require such huge amounts of 
work as DTS 18661 or ISO 24747 implementation - where one reported bug 
often shows up lots of related bugs not previously in Bugzilla, that also 
need to be fixed - rather than trying to find time for larger libm 
projects (and I'm also mostly leaving aside libm bugs in areas where 
others have shown interest in fixing them, such as performance or errno 
handling).

(The present functions, producing correctly-rounded results only for 
round-to-nearest, would not of course meet the requirements for functions 
such as crsin, although it's probably possible to adapt them by just doing 
a little bit of final arithmetic in the original rounding mode, having 
done the intermediate computations to produce a higher-precision result in 
round-to-nearest.)

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