Editing GNU MPFR

{{Short description|C library for arbitrary-precision floating-point arithmetic}}
{{Infobox software
| name = GNU MPFR
| title = GNU MPFR
| logo = Mpfr.svg
| logo size = 180px
| screenshot = GNOME Calculator 41.1.png
| caption = GNOME Calculator, which uses MPFR as of version 41.1
| collapsible = 
| author = 
| developer = [[GNU Project]] ([[INRIA]] and others)
| released = {{Start date and age|2000|02|04}}<!-- This was the first public release 0.4 (seen as close enough to 1.0 to be considered for this parameter). -->
| discontinued = 
| latest release version = 4.2.2
| latest release date = {{Start date and age|2025|3|20}}
| latest preview version = 
| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} -->
| programming language = [[C (programming language)|C]]
| operating system = [[Cross-platform]]
| platform = 
| size = 
| language = 
| genre = [[Mathematical software]]
| license = [[GNU Lesser General Public License|LGPL]]
| website = {{URL|https://www.mpfr.org/}}
}}
{{Portal|Free and open-source software}}
The '''GNU Multiple Precision Floating-Point Reliable Library''' ('''GNU MPFR''') is a [[GNU]] portable [[C (programming language)|C]] [[Library (computing)|library]] for [[Arbitrary-precision arithmetic|arbitrary-precision]] binary [[Floating-point arithmetic|floating-point]] computation with [[rounding#Table-maker's dilemma|correct rounding]], based on [[GNU Multiple Precision Arithmetic Library|GNU Multi-Precision Library]].<ref>{{cite journal
|first1 = L. |last1 = Fousse
|first2 = G. |last2 = Hanrot
|first3 = V. |last3 = Lefèvre
|first4 = P. |last4 = Pélissier
|first5 = P. |last5 = Zimmermann
|title = MPFR: A multiple-precision binary floating-point library with correct rounding
|journal = ACM Transactions on Mathematical Software 
|year = 2007 |volume = 33 |number = 2 |pages = 13:1–15
|doi = 10.1145/1236463.1236468
|s2cid = 9641003
}}
</ref><ref name="higham">{{cite web |title=The Rise of Mixed Precision Arithmetic |url=https://nhigham.com/2015/10/08/the-rise-of-mixed-precision-arithmetic/ |first=Nick |last=Higham |date=October 8, 2015 |access-date=May 23, 2020}}</ref>

==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]].

==References==
{{reflist}}

==External links==
* [https://www.mpfr.org/ Official MPFR web site]

{{DEFAULTSORT:Mpfr}}
[[Category:C (programming language) libraries]]
[[Category:Computer arithmetic]]
[[Category:Free software programmed in C]]
[[Category:GNU Project software]]
[[Category:Numerical libraries]]
[[Category:Software using the GNU Lesser General Public License]]