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Subject: [Bug libquadmath/105101] incorrect rounding for sqrtq
Date: Sat, 09 Apr 2022 10:23:39 +0000
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https://gcc.gnu.org/bugzilla/show_bug.cgi?id=3D105101

--- 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
>=20
> #ifdef HAVE_SQRTL
>   {
>     long double xl =3D (long double) x;
>     if (xl <=3D LDBL_MAX && xl >=3D LDBL_MIN)
>       {
>         /* Use long double result as starting point.  */
>         y =3D (__float128) sqrtl (xl);
>=20
>         /* One Newton iteration.  */
>         y -=3D 0.5q * (y - x / y);
>         return y;
>       }
>   }
> #endif
>=20
> 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=20
> 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).=