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Copyright 1999, 2001-2020 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. 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 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.