GNU MPFR: Difference between revisions

GNU MPFR
	GNOME Calculator, which uses MPFR as of version 41.1
Developer(s)	GNU Project (INRIA and others)
Initial release	February 4, 2000; 24 years ago
Stable release	4.2.1 / August 22, 2023; 10 months ago
Repository	gitlab.inria.fr/mpfr/mpfr.git ;
Written in	C
Operating system	Cross-platform
Type	Mathematical software
License	LGPL
Website	www.mpfr.org

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The GNU Multiple Precision Floating-Point Reliable Library (GNU MPFR) is a GNU portable C library for arbitrary-precision binary floating-point computation with correct rounding, based on GNU Multi-Precision Library.^[1]^[2]

Library[edit]

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.^[3] This is done by copying the ideas from the 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 zeros (+0 and −0), infinities and not-a-number (a single NaN is supported: MPFR does not differentiate between quiet NaNs and signaling NaNs).
Each number has its own 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 in natural base, base 2 and base 10, the log(1+x) and exp(x)−1 functions (log1p and expm1), the six trigonometric and hyperbolic functions and their inverses, the gamma, zeta and error functions, the arithmetic–geometric mean, the power (x^y) function. All those functions are correctly rounded over their complete range.
Subnormal numbers are not supported, but can be emulated with the mpfr_subnormalize function.

MPFR is not able to track the accuracy of numbers in a whole program or expression; this is not its goal. Interval arithmetic packages like Arb,^[4] MPFI,^[5] or Real RAM implementations like iRRAM,^[6] 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).^[7] Other software uses MPFR, such as ALGLIB, CGAL, FLINT, GNOME Calculator, the Julia language implementation, the Magma computer algebra system, Maple, GNU MPC, and GNU Octave.

References[edit]

^ Fousse, L.; Hanrot, G.; Lefèvre, V.; Pélissier, P.; Zimmermann, P. (2007). "MPFR: A multiple-precision binary floating-point library with correct rounding". ACM Transactions on Mathematical Software. 33 (2): 13:1–15. doi:10.1145/1236463.1236468. S2CID 9641003.
^ Higham, Nick (October 8, 2015). "The Rise of Mixed Precision Arithmetic". Retrieved May 23, 2020.
^ "Frequently asked questions about MPFR: 1. What are the differences between MPF from GMP and MPFR?".
^ "Arb, a C library for arbitrary-precision ball arithmetic". Retrieved May 31, 2022.
^ "MPFI Project". GitLab at Inria. Retrieved May 31, 2022.
^ "iRRAM, a software library for exact real arithmetic". Retrieved May 31, 2022.
^ "GCC 4.3 Release Series: Changes, New Features, and Fixes". 2012-11-02. Retrieved September 25, 2013.

External links[edit]

Official MPFR web site

[1] Fousse, L.; Hanrot, G.; Lefèvre, V.; Pélissier, P.; Zimmermann, P. (2007). "MPFR: A multiple-precision binary floating-point library with correct rounding". ACM Transactions on Mathematical Software. 33 (2): 13:1–15. doi:10.1145/1236463.1236468. S2CID 9641003.

[higham-2] Higham, Nick (October 8, 2015). "The Rise of Mixed Precision Arithmetic". Retrieved May 23, 2020.

[3] "Frequently asked questions about MPFR: 1. What are the differences between MPF from GMP and MPFR?".

[4] "Arb, a C library for arbitrary-precision ball arithmetic". Retrieved May 31, 2022.

[5] "MPFI Project". GitLab at Inria. Retrieved May 31, 2022.

[6] "iRRAM, a software library for exact real arithmetic". Retrieved May 31, 2022.

[7] "GCC 4.3 Release Series: Changes, New Features, and Fixes". 2012-11-02. Retrieved September 25, 2013.

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@@ Line 1: / Line 1: @@
+{{Short description|C library for arbitrary-precision floating-point arithmetic}}
 {{Infobox software
-| name  = GNU MPFR
+| name = GNU MPFR
-| title  = GNU MPFR
+| title = GNU MPFR
-| logo  = Mpfr.svg
+| logo = Mpfr.svg
-| logo size  = 180px
+| logo size = 180px
-| screenshot  = <!-- [[File: ]] -->
+| screenshot = GNOME Calculator 41.1.png
-| caption  =
+| caption = GNOME Calculator, which uses MPFR as of version 41.1
-| collapsible   =
+| collapsible =
+| author =
+| developer = [[GNU Project]] ([[INRIA]] and others)
-| author =
+| 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). -->
-| developer  = [[INRIA]] and others
+| discontinued =
-| released = <!-- {{Start date|YYYY|MM|DD|df=yes/no}} -->
+| latest release version = 4.2.1
-| discontinued  =
-| latest release version = 4.0.2
+| latest release date = {{Start date and age|2023|8|22}}
-| latest release date = {{Start date and age|2019|1|31}}
 | latest preview version =
-| latest preview date  = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} -->
+| latest preview date = <!-- {{Start date and age|YYYY|MM|DD|df=yes/no}} -->
-| programming language =
+| programming language = [[C (programming language)|C]]
-| operating system  =
+| operating system = [[Cross-platform]]
-| platform  =
+| platform =
-| size  =
+| size =
-| language  =
+| language =
+| genre = [[Mathematical software]]
-| status =
+| license = [[GNU Lesser General Public License|LGPL]]
-| genre  = [[Mathematical software]]
+| website = {{URL|https://www.mpfr.org/}}
-| 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
-'''GNU MPFR''' ('''GNU Multiple Precision Floating-Point Reliably'''<ref>{{cite journal
 |first1 = L. |last1 = Fousse
 |first2 = G. |last2 = Hanrot
@@ Line 33: / Line 33: @@
 |first5 = P. |last5 = Zimmermann
 |title = MPFR: A multiple-precision binary floating-point library with correct rounding
-|journal = ACM Transactions on Mathematical Software (TOMS)
+|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>
-</ref>) is a [[GNU]] portable [[C (programming language)|C]] [[Library (computing)|library]] for [[bignum|arbitrary-precision]] binary [[floating-point]] computation with [[rounding#The table-maker's dilemma|correct rounding]], based on [[GNU Multi-Precision Library]]. The 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. This is done by copying the ideas from the [[IEEE floating-point standard|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 zeros ([[−0]]), infinities and [[NaN|not-a-number]] (a single NaN is currently supported).
-* Each number has its own [[Precision (arithmetic)|precision]] (in bits since MPFR uses [[radix]] 2). The floating-point results are correctly rounded to the precision of the target variable, in any of the four [[IEEE floating-point standard|IEEE-754]] rounding modes.
-* 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 function|trigonometric]] and [[Hyperbolic function|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.
-* [[Denormal number|Subnormals]] are not supported, but can be emulated with the <code>mpfr_subnormalize</code> function.
+==Library==
-MPFR is not able to track the [[accuracy]] of numbers in a whole program or expression; this is not its goal. [[Interval arithmetic]] packages like [http://arblib.org/ Arb], [https://gforge.inria.fr/projects/mpfi/ MPFI], or [[Real RAM]] implementations like [http://irram.uni-trier.de/ iRRAM], which may be based on MPFR, can do that for the user.
+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
@@ Line 49: / Line 55: @@
 | 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]].
-| accessdate=2013-09-25}}</ref>
 ==References==
@@ Line 56: / Line 62: @@
 ==External links==
 * [https://www.mpfr.org/ Official MPFR web site]
-* [https://gforge.inria.fr/projects/mpfr/ MPFR project page]
 {{DEFAULTSORT:Mpfr}}
-[[Category:C libraries]]
+[[Category:C (programming language) libraries]]
 [[Category:Computer arithmetic]]
 [[Category:Free software programmed in C]]