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

["bugdal at aerifal dot cx" <sourceware-bugzilla at sourceware dot org>]

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

--- Comment #43 from Rich Felker <bugdal at aerifal dot cx> 2013-04-29 17:30:14 UTC ---
I don't have a copy of the latest IEEE 754 on hand (there's no free online
version), but the consensus among implementors seems to be that a few special
functions (such as sqrt) require correct rounding, and that the remaining
functions (mostly transcendental) are required to give results with less than
1ulp of error. If sin(0x1p1000) is computed with incorrect argument reduction,
it may have up to approximately 1e16 ulp error.

Moreover, the C standard specifies:

"2 The sin functions compute the sine of x (measured in radians).

Returns

3 The sin functions return sin x."

Without annex F, the C standard places no requirements on the precision or
accuracy of floating point results (e.g. 2.0+2.0==5.0 is legal), but annex F
recommends IEEE conforming behavior.

If anyone else can provide some better citations, they'd be welcome.

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