[1][2] 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: 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).