GMP license: COPYING file (GPL) and LGPLv3

[pesec.il]

Hello, colleagues.
I see that the GMP site (https://gmplib.org/manual/Copying.html) tells
GMP has LGPL license:

    ---
    The precise conditions of the license for the GNU MP library are
    found in the Lesser General Public License version 3 that
    accompanies the source code, see COPYING.LIB. Certain demonstration
    programs are provided under the terms of the plain General Public
    License version 3, see COPYING.
    ---

But when I look at the README file in GMP 5.1.3 source distribution, it
says:

    ---
    GNU MP is free software and may be freely copied on the terms
    contained in the files COPYING.LIB and COPYING (most of GNU MP
    is under the former, some under the latter).
    ---

(COPYING is GPLv3, COPYING.LIB is LGPLv3).

So, the README file does not explicitly say what is licensed under GPL
and what is licensed under LGPL.

Now the questions:

1. Is the library itself under LGPLv3?
2. What is licensed under GPL: just demos/tests, or anything else?
3. Will there by any such statement in the README file,
    in the distribution (not on the web site)?
4. Shall I file a bug for the README file fix (to
    explicitly declare what is licensed under GPL)?

Yours,
- Alexey.