Editing GNU MPFR (section)

==Library==
MPFR's computation is both efficient and has a well-defined semantics: the functions are completely specified on all the possible operands and the results do not depend on the platform.<ref>{{cite web |url=https://www.mpfr.org/faq.html#mpfr_vs_mpf |title=Frequently asked questions about MPFR: 1. What are the differences between MPF from GMP and MPFR? }}</ref> This is done by copying the ideas from the [[IEEE 754|ANSI/IEEE-754]] standard for fixed-precision floating-point arithmetic (correct rounding and exceptions, in particular). More precisely, its main features are:
* Support for special numbers: [[signed zero]]s (+0 and −0), [[Infinity#Computing|infinities]] and [[NaN|not-a-number]] (a single NaN is supported: MPFR does not differentiate between quiet NaNs and signaling NaNs).
* Each number has its own [[Precision (computer science)|precision]] (in bits since MPFR uses [[radix]] 2). The floating-point results are correctly rounded to the precision of the target variable, in one of the five supported rounding modes (including the four from [[IEEE 754-1985]]).
* Supported functions: MPFR implements all mathematical functions from [[C99]] and other usual mathematical functions: the [[logarithm]] and [[exponential function|exponential]] in natural base, base 2 and base 10, the log(1+x) and exp(x)−1 functions (<code>log1p</code> and <code>expm1</code>), the six [[Trigonometric functions|trigonometric]] and [[hyperbolic functions|hyperbolic]] functions and their inverses, the [[Gamma function|gamma]], [[Riemann zeta function|zeta]] and [[error function]]s, the [[arithmetic–geometric mean]], the [[exponentiation|power]] (x<sup>y</sup>) function. All those functions are correctly rounded over their complete range.
* [[Subnormal number]]s are not supported, but can be emulated with the <code>mpfr_subnormalize</code> function.

MPFR is not able to track the [[accuracy and precision|accuracy]] of numbers in a whole program or expression; this is not its goal. [[Interval arithmetic]] packages like Arb,<ref>{{cite web | url=https://arblib.org/ | title=Arb, a C library for arbitrary-precision ball arithmetic | access-date=May 31, 2022}}</ref> MPFI,<ref>{{cite web | url=https://gitlab.inria.fr/mpfi/mpfi/ | title=MPFI Project | website=GitLab at Inria | access-date=May 31, 2022}}</ref> or [[Real RAM]] implementations like iRRAM,<ref>{{cite web | url=http://irram.uni-trier.de/ | title=iRRAM, a software library for exact real arithmetic | access-date=May 31, 2022}}</ref> which may be based on MPFR, can do that for the user.

MPFR is dependent upon the [[GNU Multiple Precision Arithmetic Library]] (GMP).

MPFR is needed to build the [[GNU Compiler Collection]] (GCC).<ref>{{cite web
| url=https://gcc.gnu.org/gcc-4.3/changes.html#mpfropts
| title=GCC 4.3 Release Series: Changes, New Features, and Fixes
| date=2012-11-02
| access-date=September 25, 2013}}</ref> Other software uses MPFR, such as [[ALGLIB]], [[CGAL]], [[Fast Library for Number Theory|FLINT]], [[GNOME Calculator]], the [[Julia (programming language)|Julia language]] implementation, the [[Magma (computer algebra system)|Magma computer algebra system]], [[Maple (software)|Maple]], GNU MPC, and [[GNU Octave]].