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mpfr: new raspbian lacks libmpfr.so.4. Use mpfr-3.1.4 to build correc…

…t version to run the compiler correctly.
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matthiasseemoo committed Jul 4, 2019
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Authors of MPFR (in chronological order of initial contribution):

Guillaume Hanrot Main author
Fabrice Rouillier Original version of mul_ui.c, gmp_op.c
Paul Zimmermann Main author
Sylvie Boldo Original version of agm.c and log.c
Jean-Luc Rémy Original version of zeta.c
Emmanuel Jeandel Original version of exp3.c, const_pi.c, sincos.c
Mathieu Dutour acos.c, asin.c, atan.c and early gamma.c
Vincent Lefèvre Main author
David Daney Hyperbolic and inverse hyperbolic functions, base-2
and base-10 exponential and logarithm, factorial
Alain Delplanque Rewritten get_str.c
Ludovic Meunier Error function (erf.c)
Patrick Pélissier Main author
Laurent Fousse Original version of sum.c
Damien Stehlé Function mpfr_get_ld_2exp
Philippe Théveny Main author
Sylvain Chevillard Original version of ai.c

The main authors are included in the MPFR mailing-list <mpfr@inria.fr>.
This is the preferred way to contact us. For further information, please
look at the MPFR web page <http://www.mpfr.org/>.
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Copyright 1999, 2001-2016 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.

##############################################################################

Known bugs:

* The overflow/underflow exceptions may be badly handled in some functions;
specially when the intermediary internal results have exponent which
exceeds the hardware limit (2^30 for a 32 bits CPU, and 2^62 for a 64 bits
CPU) or the exact result is close to an overflow/underflow threshold.

* Under Linux/x86 with the traditional FPU, some functions do not work
if the FPU rounding precision has been changed to single (this is a
bad practice and should be useless, but one never knows what other
software will do).

* Some functions do not use MPFR_SAVE_EXPO_* macros, thus do not behave
correctly in a reduced exponent range.

* Function hypot gives incorrect result when on the one hand the difference
between parameters' exponents is near 2*MPFR_EMAX_MAX and on the other hand
the output precision or the precision of the parameter with greatest
absolute value is greater than 2*MPFR_EMAX_MAX-4.

Potential bugs:

* Possible incorrect results due to internal underflow, which can lead to
a huge loss of accuracy while the error analysis doesn't take that into
account. If the underflow occurs at the last function call (just before
the MPFR_CAN_ROUND), the result should be correct (or MPFR gets into an
infinite loop). TODO: check the code and the error analysis.

* Possible integer overflows on some machines.

* Possible bugs with huge precisions (> 2^30).

* Possible bugs if the chosen exponent range does not allow to represent
the range [1/16, 16].

* Possible infinite loop in some functions for particular cases: when
the exact result is an exactly representable number or the middle of
consecutive two such numbers. However for non-algebraic functions, it is
believed that no such case exists, except the well-known cases like cos(0)=1,
exp(0)=1, and so on, and the x^y function when y is an integer or y=1/2^k.

* The mpfr_set_ld function may be quite slow if the long double type has an
exponent of more than 15 bits.

* mpfr_set_d may give wrong results on some non-IEEE architectures.

* Error analysis for some functions may be incorrect (out-of-date due
to modifications in the code?).

* Possible use of non-portable feature (pre-C99) of the integer division
with negative result.

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