correct rounding or not?

[paul zimmermann <Paul dot Zimmermann at inria dot fr>]

       Hi,

in sysdeps/ieee754/dbl-64 one can find code coming from IBM's
Accurate Mathematical Library (libultim), with comments claiming
for correct rounding, for example in s_sin.c one can read around
lines 194-197:

/*******************************************************************/
/* An ultimate sin routine. Given an IEEE double machine number x   */
/* it computes the correctly rounded (to nearest) value of sin(x)  */
/*******************************************************************/
...
__sin (double x)

However, it appears that the __sin function is not correctly rounded,
for example for x=8.5546900000006210e-01 it gives 7.5487859961632653e-01
whereas the correct rounding is 7.5487859961632664e-01 (according to mpfr).

Maybe the original code from libultim was modified, in particular the
code that guarantees correct rounding (rounding test + slow path) was
removed?

Anyway, I believe the comments should be modified to accurately
describe what the current code does.

Best regards,
Paul Zimmermann