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1. Introduction to MPFR
MPFR is a portable library written in C for arbitrary precision arithmetic
on floating-point numbers. It is based on the GNU MP library.
It aims to extend the class of floating-point numbers provided by the
GNU MP library by a precise semantics. The main differences
with the mpf class from GNU MP are:
- the MPFR code is portable, i.e. the result of any operation
does not depend (or should not) on the machine word size
mp_bits_per_limb(32 or 64 on most machines); - the precision in bits can be set exactly to any valid value for each variable (including very small precision);
- MPFR provides the four rounding modes from the IEEE 754-1985 standard.
In particular, with a precision of 53 bits, MPFR should be able to
exactly reproduce all computations with double-precision machine
floating-point numbers (e.g., double type in C, with a C
implementation that rigorously follows Annex F of the ISO C99 standard
and FP_CONTRACT pragma set to OFF) on the four arithmetic
operations and the square root, except the default exponent range is much
wider and subnormal numbers are not implemented (but can be emulated).
This version of MPFR is released under the GNU Lesser General Public License, Version 2.1 or any later version. It is permitted to link MPFR to most non-free programs, as long as when distributing them the MPFR source code and a means to re-link with a modified MPFR library is provided.