[Bug math/13381] rounding problem wih sincosl

["vincent-srcware at vinc17 dot net" <sourceware-bugzilla@sourceware.org>]

http://sourceware.org/bugzilla/show_bug.cgi?id=13381

--- Comment #10 from Vincent Lefèvre <vincent-srcware at vinc17 dot net> 2011-12-23 11:01:30 UTC ---
I agree that this bug here can be seen as invalid, as long as the error is not
greater than the documented error bound. It's even "normal" that sincosl
doesn't return the same result as sinl and cosl, as the algorithm is different
and the goal of such a hardware implementation is to provide a result quickly,
though not highly accurate.

Now, there could be two valid related bugs:

1. As these hardware functions seem to be completely wrong for large arguments
(on both Intel and AMD), the glibc should not use them in such cases. At least,
it should provide an option so that it can be compiled to use a software
implementation. Note: though relatively fast hardware range reduction is
possible, I'm sure that was the intent of these hardware instructions when they
were introduced in the 80's (?). I mean that blindly using these hardware
instructions in a system library (i.e. without knowing the application) could
be seen as a misuse of these instructions.

2. The IEEE 754-2008 standard recommends correct rounding. So, a RFE to have
correct rounding would be valid, but perhaps wontfix for the extended precision
(not standard, its primary goal being to ease accurate implementations of the
double precision). For the double precision, unless this has been fixed, sincos
is affected by this problem, which affects code using sin and cos compiled by
GCC; see

  http://www.vinc17.net/research/slides/sieste2010.pdf

Slides 11-15 for this point.

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