creating math constants of variable precision using Boost mpfr_float, such as pi or e

Question

I am using Boost.Multiprecision for wrappers around the mpfr backend, and I am having some trouble creating pi (and e or any other math constant) to my desired precision. I feel like what I want to do should be possible, because of the use of Boost.Math for constants on a tutorial page for Boost.Multiprecision. In the tutorial, they use fixed-precision numbers of types such as cpp_dec_float_50 -- I want to do it with variable_precision mpfr_float. Check out the following code:

#include <boost/multiprecision/mpfr.hpp>
#include <boost/math/constants/constants.hpp>
#include <iostream>

...
int main() {
    boost::multiprecision::mpfr_float::default_precision(1000);
    boost::multiprecision::mpfr_float pi = boost::math::constants::pi<boost::multiprecision::mpfr_float>();
    std::cout << std::fixed;
    std::cout.precision(1000);
    std::cout << pi.precision() << " " << pi << std::endl;
}

The result is a number, pi, which has precision 1000, but only has ~165 digits of pi, as evidenced by the result of the output statements, which confirm that my pi is of precision 1000, and prints about 165 correct digits, and ~835 zeros. this is clearly wrong.

is it possible to make a boost::multiprecision::mpfr_float at high precision populated with constants from boost::math::constants?

Note that I need to use a variable precision type, and that other high-but-fixed-precision types are not an option. I must be able to change precision on the fly at runtime.

Hullda

Answer 1

The constants embedded in the Boost headers have a limited precision, and you've hit that limit. If you need a higher-precision version of pi (for instance), you'll need to bring it yourself.

For instance, the definition of boost::math::constants::pi in the headers is:

  BOOST_DEFINE_MATH_CONSTANT(pi, 3.141592653589793238462643383279502884e+00, "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651e+00")

— https://github.com/boostorg/math/blob/master/include/boost/math/constants/constants.hpp

(This definition only gives 110 digits past the decimal place, by the way. Any digits you're getting beyond that are likely to be incorrect!)

Ginsburg

this does indeed solve my problem, and points to misleading information in the boost tutorial documentation, which naively leads me to believe that if I were using a long fixed-precision number, i would be able to fully populate it with those constants... thanks for referencing the documentation. do you think this merits a filing bugreport with boost? or is this solely up to me? – Hullda