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mpfr
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Vincent Lefevre
Updated the "Contributed" lines.
02 фев 2025, 02:39
02 фев 2025, 02:39
a774f60
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Copyright 1999, 2001-2025 Free Software Foundation, Inc. Contributed by the Pascaline 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/>. ############################################################################## 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.