Programming

mpfr::real

About

The class mpfr::real is a high-level C++ wrapper for the GNU MPFR library, “a C library for multiple-precision floating-point computations with correct rounding”.

The objects of mpfr::real can (almost) be used like doubles or other fundamental floating-point types, thus avoiding the use of C functions to manipulate MPFR's low-level data type directly. In addition to all arithmetic and comparison operators available for fundamental floating-point types, mpfr::real also supports the set of mathematical functions for double from math.h/cmath. Finally, std::istream operator >> and std::ostream operator << are implemented for mpfr::reals. This allows to substitute double with mpfr::real with no further modifications of the code in many cases.

Example

The following shows an example of how to use mpfr::real.

#include "real.hpp"

int main () {
  mpfr::real<4096> a = "1.23456789";
  mpfr::real<4096> b = 5.;
  std::cout << sin(2 * pow(a, b)) << std::endl;

  return 0;
}

The calculation is done with mpfr::reals with 4096 bits of precision (see the template argument of mpfr::real). The rounding used in the calculation defaults to MPFR_RNDN. An alternative rounding supported by the MPFR library could have been set as second template argument of mpfr::real.

The variable a is initialized from the char[] "1.23456789". If the quotation marks had been omitted, the token 1.23456789 would have been interpreted as double and a would have been initialized from that double. This would have been resulted in a truncation of precision of the number 1.23456789 to the precision of a double (e.g., 53 bits) and there would have been a loss of precision in the initialization of a.

The variable b is initialized from the double 5., which has an exact representation. Hence, there is no loss in precision. The last line calculates a to the power of b, multiplies it with the int 2 using the optimized multiplication function of MPFR's data type with ints, and calculates the sine of the result. The result type of the whole calculation is a mpfr::real<4096>, which is finally output (with the configured precision of std::cout).

Download

Although some testing has been done, mpfr::real is still alpha software and may contain serious errors. If you experience problems, please drop me a mail.

Brian Gladman pointed out several problems with Microsoft Visual C++. Temporarily, there will be two different headers for G++ and Visual C++. I aim at publishing a new, single version with extended documentation that will work with all major compiler soon. Make sure you pick the right one.

Comparison with Other MPFR C++ Wrappers

There are already some C++ wrappers for the MPFR library, most notably Pavel Holoborodko's MPFR C++ package, which provides the class mpreal with a very similar functionality as mpfr::real. The main differences between mpreal and mpfr::real are due to different design decisions:

The class mpfr::real is a template class with two template parameters: The first one is an integer specifying the precision (in bits) and the second one is the rounding used by the MPFR library (defaults to MPFR_RNDN). Hence, each mpfr::real with different precision and/or rounding effectively constitutes a new data type. As a result, the precision of a mpfr::real must be known during compile time and cannot be changed or set during runtime. In contrast, mpreal is not a template class and the precision as well as the rounding of mpreals can be changes during runtime.

However, the use of template metaprogramming techniques in mpfr::real provides some advantages: Firstly, they allow for optimizing away the C++ class overhead during compile time such that the generated code is basically identical to the code that would have been generated when using the MPFR C interface. Secondly, it allows for fine-tuning the support of other data types (implicit/explicit type conversion, enabling/disabling of operators or mathematical functions, etc.) in mpfr::real by use of type traits. This includes the handling of mpfr::reals with different precision in the same expression.

Last but not least, mpfr::real provides the complete set of mathematical functions as known from math.h/cmath, which might be useful in some cases. (Still, the “typical” functions are also supported by mpreal.)