Determining the “optimal” common numeric type in a template parameter pack

Question

What is the best way to determine a common numeric type in a template parameter pack with:

1. the smallest size,
2. no loss of precision, a

Answer 1

You could use Boost Integer to select the proper cases.

• http://www.boost.org/doc/libs/1_54_0/libs/integer/doc/html/boost_integer/integer.html#boost_integer.integer.sized

Ignoring for a moment the cases on non-integral element types, here's a quick test of the proposed cases (GCC doesn't have int128_t as it appears):

Live on Coliru

#include 
#include 
#include 
#include 
#include 
#include 

using namespace boost;

namespace best_fit_
{
    // wrappers around Boost Integer http://www.boost.org/doc/libs/1_54_0/libs/integer/doc/html/boost_integer/integer.html#boost_integer.integer.sized
    template  struct select_int;

    template  struct select_int {
        using type = typename boost::int_t::least;
    };

    template  struct select_int {
        using type = typename boost::uint_t::least;
    };

    // query helper
    struct digits {
        template  using apply = mpl::int_::digits>;
    };
}

template 
struct best_common_integral
{
    private:
        using Ints = mpl::vector;
        using Bits = typename mpl::transform::type;

        template 
            struct is_signed { static constexpr bool value = std::numeric_limits::is_signed; };

        using max  = typename mpl::deref::type>::type;

        // sigh, there is no `mpl::any`, AFAICT
        using sign = typename mpl::fold<
                    Ints, 
                    mpl::bool_, 
                    mpl::if_, mpl::bool_, mpl::_1>
                >::type;
    public:
        using type = typename best_fit_::select_int::type;
};

#include 
#include 
#include 

int main()
{
    using case1 = best_common_integral;
    using case2 = best_common_integral;
    using case3 = best_common_integral;
    using case4 = best_common_integral;
    using case5 = best_common_integral;

    //assert(typeid(case1::type) == typeid(double));
    assert(typeid(case2::type) == typeid(unsigned long));
    assert(typeid(case3::type) == typeid(signed long));
    assert(typeid(case4::type) == typeid(signed long));
    //assert(typeid(case5::type) == typeid(int128_t (maybe)));
}