https://gcc.gnu.org/bugzilla/show_bug.cgi?id=105101
--- Comment #5 from Thomas Koenig <tkoenig at gcc dot gnu.org> ---
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.
I believe we can at least fix that before the gcc 12 release, by
simply removing the code I quoted.
