The GNU Multiple Precision Floating-Point Reliable Library (GNU MPFR) is a GNU portable C library for arbitrary-precision binary

floating-point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can b ...

computation with correct rounding, based on

GNU Multi-Precision Library GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones imp ...

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. 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 Nan or NAN may refer to: Places China * Nan County, Yiyang, Hunan, China * Nan Commandery, historical commandery in Hubei, China Thailand * Nan Province ** Nan, Thailand, the administrative capital of Nan Province * Nan River People Given name ...

(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 In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is t ...

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 Gamma (uppercase , lowercase ; ''gámma'') is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter re ...

, zeta and

error function In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as: :\operatorname z = \frac\int_0^z e^\,\mathrm dt. This integral is a special (non-elementary ...

s, 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 Accuracy and precision are two measures of ''observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each other ...

of numbers in a whole program or expression; this is not its goal. Interval arithmetic packages like Arb, MPFI, or

Real RAM In computing, especially computational geometry, a real RAM (random-access machine) is a mathematical model of a computer that can compute with exact real numbers instead of the binary fixed point or floating point numbers used by most actual comp ...

implementations like iRRAM, 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). Other software uses MPFR, such as ALGLIB,

CGAL The Computational Geometry Algorithms Library (CGAL) is an open source software library of computational geometry algorithms. While primarily written in C++, Scilab bindings and bindings generated with SWIG (supporting Python and Java for now) ar ...

, FLINT,

GNOME Calculator GNOME Calculator, formerly known as gcalctool, is the software calculator integrated with the GNOME desktop environment. It is programmed in C and Vala and part of the GNOME Core Applications. Views * ''Basic'' – interface for basic arithmet ...

, the

Julia language Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programmin ...

implementation, the Magma computer algebra system, Maple, GNU MPC, and GNU Octave.

References

External links

Official MPFR web site
{{DEFAULTSORT:Mpfr C (programming language) libraries Computer arithmetic Free software programmed in C GNU Project software Numerical libraries Software using the LGPL license