Integer conversions, C++ (clang)

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#include <iostream>
#include <type_traits>
#include <limits>

/**
 * The size of a integer types domain is 2^digits - 1
 * The ratio between two types is then (2^d1 - 1) / (2^d2 - 1) 
 * which for power of 2 number of digits can be written as:
 *
 * (-1 + x)(1+x^1)(1+x^2)(1+x^4)(1+x^8)...(1+x^d1/2)
 * --------------------------------------------------
 * (-1 + x)(1+x^1)(1+x^2)(1+x^4)(1+x^8)...(1+x^d2/2)
 *
 * assuming that d1 > d2 can be simplified to:
 *
 * (1+x^d2)...(1+x^d1/2)
 */

/* Recursive implementation 
 *             / (2^D1+1) * f(D1*2, D2) if D1 != D2
 * f(D1,D2) = {
 *             \ 1                      if D1 == D2 
 */
template <typename T, size_t D1, size_t D2>
struct ratioImpl {
    static const T value = ((T{1} << D2) + T{1}) * ratioImpl<T, D1, D2*2>::value;
};

// termination. 
template <typename T, size_t D>
struct ratioImpl<T, D, D>{
    static const T value = T{1};
};
/*
 * Calculate the ratio between to Integer domain sizes. 
 * The number of digits in "To" should always be the larger 
 * or equal to the number digits in "From".
 */
template <typename To, typename From>
struct ratio {
    static_assert(std::numeric_limits<To>::digits >= std::numeric_limits<From>::digits, "Invalid type order: To is smaller then From");
    static const To value = ratioImpl<To, std::numeric_limits<To>::digits, std::numeric_limits<From>::digits>::value;
};

int main() { 
    std::cout << "char->char         " << (int)ratio<unsigned char, unsigned char>::value << std::endl;
    std::cout << "char->short        " << ratio<unsigned short, unsigned char>::value << std::endl;
    std::cout << "char->int          " << ratio<unsigned int, unsigned char>::value << std::endl;
    std::cout << "char->longlong     " << ratio<unsigned long long, unsigned char>::value << std::endl;
    std::cout << std::endl;
    std::cout << "short->char        " << 1.0 / ratio<unsigned short, unsigned char>::value << std::endl;
    std::cout << "short->short       " << ratio<unsigned short, unsigned short>::value << std::endl;
    std::cout << "short->int         " << ratio<unsigned int, unsigned short>::value << std::endl;
    std::cout << "short->longlong    " << ratio<unsigned long long, unsigned short>::value << std::endl;
    std::cout << std::endl;
    std::cout << "int->char          " << 1.0 / ratio<unsigned int, unsigned char>::value << std::endl;
    std::cout << "int->short         " << 1.0 / ratio<unsigned int, unsigned short>::value << std::endl;
    std::cout << "int->int           " << ratio<unsigned int, unsigned int>::value << std::endl;
    std::cout << "int->longlong      " << ratio<unsigned long long, unsigned int>::value << std::endl;
    std::cout << std::endl;
    std::cout << "longlong->char     " << 1.0 / ratio<unsigned long long, unsigned char>::value << std::endl;
    std::cout << "longlong->short    " << 1.0 / ratio<unsigned long long, unsigned short>::value << std::endl;
    std::cout << "longlong->int      " << 1.0 / ratio<unsigned long long, unsigned int>::value << std::endl;
    std::cout << "longlong->longlong " << ratio<unsigned long long, unsigned long long>::value << std::endl;
}

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Compilation time: 0.62 sec, absolute running time: 0.13 sec, cpu time: 0 sec, memory peak: 3 Mb, absolute service time: 0,76 sec