GNU MPFR (for GNU Multiple Precision Floating-Point Reliably) is a portable C library for arbitrary-precision binary floating-point computation with 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 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 not-a-number (a single NaN is currently supported).
- 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 any of the four IEEE-754 rounding modes.
- Supported functions: MPFR implements all mathematical functions from C99: the logarithm and exponential in natural base, base 2 and base 10, the log(1+x) and exp(x)-1 functions (
log1pandexpm1), the six trigonometric and hyperbolic functions and their inverses, the gamma, zeta and error functions, the arithmetic geometric mean, the power (xy) function. All those functions are correctly rounded over their complete range. - Subnormals are not supported, but can be emulated with the
mpfr_subnormalizefunction.
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 MPFI, or Real RAM implementations like iRRAM, which may be based on MPFR, can do that for the user.