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From: "sgk at troutmask dot apl.washington.edu" <gcc-bugzilla@gcc.gnu.org>
To: gcc-bugs@gcc.gnu.org
Subject: [Bug fortran/96711] Internal Compiler Error on NINT() Function
Date: Thu, 20 Aug 2020 15:39:14 +0000
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https://gcc.gnu.org/bugzilla/show_bug.cgi?id=3D96711

--- Comment #11 from Steve Kargl <sgk at troutmask dot apl.washington.edu> =
---
On Thu, Aug 20, 2020 at 01:47:58PM +0000, bre08 at eggen dot co.uk wrote:
> https://gcc.gnu.org/bugzilla/show_bug.cgi?id=3D96711
>=20
> --- Comment #10 from B Eggen <bre08 at eggen dot co.uk> ---
> I've been experimenting with the suggested work-around
>=20
> m =3D anint(y)
>=20
> This works for larger numbers, even in quad precision, however, it breaks=
 down
> a long way before the integer*16 range is exhausted, consider the code be=
low,
> which starts with 2^113 and tries to double it, minus 1.  The minus 1 is =
not
> taking effect:
>=20

Of course, that is going to fail if you want an exact result.
REAL(16) is a floating point format, which has 113 digits of
precision.  This means that integers less than 2**113 are
exactly representable as REAL(16) floating point numbers.
When you double (2._16)**113 to (2._16)**114, that is a prefectly
fine REAL(16) floating point number.  Subtracting 1._16
from (2._16)**114 is a valid floating point operation.  Your
problem lies in that result is rounded, and 1._16 is less than
epsilon(1._16) in comparison to (2._16)**114.

> I guess at some point NINT() will be fixed, can anyone suggest a robust
> workaround that is valid until 2^127-1 ?

If you're trying to use floating point arithmetic in computations
and you need exact integral values up to 2**127-1, then there isn't
a REAL type that works.=20=20

If you're looking for arbitrary precision arithmetic and you
want to use Fortran, I suggest that you google "David Bailey
arithmetic".=