higher precision floating point using boost lib (higher then 16 digits)

Question

I am running a simulation of physical experiments, so I need really high floating point precision (more than 16 digits). I use Boost.Multiprecision, however I can't get a precision higher than 16 digits, no matter what I tried. I run the simulation with C++ and eclipse compiler, for example:

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

using boost::multiprecision::cpp_dec_float_50;

void main()
{
    cpp_dec_float_50 my_num= cpp_dec_float_50(0.123456789123456789123456789);
    std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
    std::cout << my_num << std::endl;
}

The output is:

0.12345678912345678379658409085095627233386039733887
                   ^

But it should be:

0.123456789123456789123456789

As you can see, after 16 digits it is incorrect. Why?

Answer 1

Your issue is here:

cpp_dec_float_50 my_num = cpp_dec_float_50(0.123456789123456789123456789);
                                            ^ // This number is a double!

The compiler does not use arbitrary-precision floating point literals, and instead uses IEEE-754 doubles, which have finite precision. In this case, the closest double to the number you have written is:

0.1234567891234567837965840908509562723338603973388671875

And printing it to the 50th decimal does indeed give the output you are observing.

What you want is to construct your arbitrary-precision float from a string instead (demo):

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

using boost::multiprecision::cpp_dec_float_50;

int main() {
    cpp_dec_float_50 my_num = cpp_dec_float_50("0.123456789123456789123456789");
    std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
    std::cout << my_num << std::endl;
}

Output:

0.123456789123456789123456789