Switch statemend variadic template expansion

Let me please consider the following synthetic example:

inline int fun2(int x) {
    return x;
}
inline int fun2(double x) {
    return 0;   
}
inline int fun2(float x) {
    return -1;   
}

int fun(const std::tuple<int,double,float>& t, std::size_t i) {
    switch(i) {
        case 0: return fun2(std::get<0>(t));
        case 1: return fun2(std::get<1>(t));
        case 2: return fun2(std::get<2>(t));
    }    
}

The question is how should I expand this to the general case

template<class... Args> int fun(const std::tuple<Args...>& t, std::size_t i) {
// ?
}

Guaranteeing that

1. fun2 can be inlined into fun
2. search complexity not worse than O(log(i)) (for large i).

It is known that optimizer usually uses lookup jump table or compile-time binary search tree when large enough switch expanded. So, I would like to keep this property affecting performance for large number of items.