Exception in cpp_int convert_to terminates program

[martindolezal]

See the following code: https://godbolt.org/z/cs6cbjnPr

#include <boost/multiprecision/cpp_int.hpp>
#include <iostream>

int main() {
    std::string strNumber = "179769313486231590617005494896502488139538923424507473845653439431848569886227202866765261632299351819569917639009010788373365912036255753178371299382143631760131695224907130882552454362167933328609537509415576609030163673758148226168953269623548572115351901405836315903312675793605327103910016259918212890625";
    boost::multiprecision::cpp_int number(strNumber);

    try {
        std::cout << number.convert_to<double>() << "\n";
    } catch (...) {
        std::cout << "some exception caught" << "\n";
    }

    std::cout << "finished" << "\n";
}

convert_to<double>() throws exception here, but it terminates the program, cannot be caught. It seems to be due to noexcept qualifier somewhere on the way, probably eval_convert_to in cpp_int/misc.hpp

The behavior change between boost 1.78 and boost 1.79.