Copyright 1999, 2001-2023 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
https://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.
  Note: Such huge precisions are not possible as they would be larger than
  MPFR_PREC_MAX, unless the types for mpfr_exp_t and/or mpfr_prec_t are
  changed (only for developers or expert users, not officially supported).

Potential bugs:

* Possible incorrect results due to internal overflow or underflow, which
  can lead to a huge loss of accuracy while the error analysis does not
  take that into account. If the overflow or underflow occurs at the last
  function call (just before the MPFR_CAN_ROUND), the (result,error bound)
  pair should be valid (or MPFR may either get into an infinite loop or
  return an incorrect result). In particular, this may not be the case if
  the last operation before MPFR_CAN_ROUND underflows to a non-zero real
  number (i.e. the minimum positive or negative number in magnitude): while
  MPFR_CAN_ROUND always returns false for singular numbers (which could be
  the consequence of an overflow or an underflow in the last operation),
  the behavior on non-zero real numbers is based on a valid error bound.
  An overflow with MPFR_RNDZ could also be an issue (though such a case
  is probably already handled correctly in the MPFR code). Note that the
  README.dev file already warns about these issues.
  TODO:
    * Check the code and the error analysis.
    * When possible, add tests near the underflow and overflow thresholds,
      using the inverse function (in a similar way to what bad_cases() does
      to build hard-to-round cases).

* Possible bugs with huge precisions (> 2^30) and a 32-bit ABI, in particular
  undetected integer overflows. TODO: use the MPFR_ADD_PREC macro.

* 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.