https://gcc.gnu.org/bugzilla/show_bug.cgi?id=105101
--- Comment #6 from Jakub Jelinek <jakub at gcc dot gnu.org> ---
(In reply to Thomas Koenig from comment #5)
> There is another, much worse, problem, reported and analyzed by "Michael S"
> on comp.arch. The code has
>
> #ifdef HAVE_SQRTL
> {
> long double xl = (long double) x;
> if (xl <= LDBL_MAX && xl >= LDBL_MIN)
> {
> /* Use long double result as starting point. */
> y = (__float128) sqrtl (xl);
>
> /* One Newton iteration. */
> y -= 0.5q * (y - x / y);
> return y;
> }
> }
> #endif
>
> which assumes that long double has a higher precision than
> normal double. On x86_64, this depends o the settings of the
> FPU flags, so a number like 0x1.06bc82f7b9d71dfcbddf2358a0eap-1024
> is corrected with 32 ULP of error because there is only a single
> round of Newton iterations if the FPU flags are set to normal precision.
That is only a problem on OSes that do that, I think mainly BSDs, no?
On Linux it should be fine (well, still not 0.5ulp precise, but not as bad as
when sqrtl is just double precision precise).
