Why isn't this call to a template ambiguous?

Question

I declare two templates, the first converts the argument x from type T to type U and the second from type U to type T. If I call cast with 10, the compiler does not complain. I think both meet the requirements to be used and therefore there should be ambiguity, is that true? This code prints 10.

#include <iostream>

template<typename T, typename U>
U cast(T x) {
    return static_cast<U>(x);
}

template<typename T, typename U>
T cast(U x) {
    return static_cast<T>(x);
}

int main() {
    std::cout << cast<int,float>(10) << '\n';
}

Answer 1

When you use cast<int, float>, both templates are considered.

template<typename T=int,typename U=float>
U cast(T x);
template<typename T=int,typename U=float>
T cast(U x);

we then substitute:

template<typename T=int,typename U=float>
float cast(int x);
template<typename T=int,typename U=float>
int cast(float x);

at this point, there are no types to deduce. So we go to overload resolution.

In one case, we can take an int and convert to float when calling cast, and in the other we take a int and convert to int when calling cast. Note I'm not looking at all into the body of cast; the body is not relevant to overload resolution.

The second non-conversion (at the point of call) is a better match, so that overload is chosen.

If you did this:

std::cout << cast<int>(10) << "\n";

things get more interesting:

template<typename T=int,typename U=?>
U cast(T x);
template<typename T=int,typename U=?>
T cast(U x);

for the first one, we cannot deduce U. For the second one we can.

template<typename T=int,typename U=?>
U cast(int x);
template<typename T=int,typename U=int>
int cast(int x);

so here we have one viable overload, and it is used.

Answer 2

The instantiation is not ambiguous because the function argument exactly matches the first template parameter: the literal 10 is an int, which is also explicitly specified for the first template type.

You can make the instantiation ambiguous when the argument type does not match the explicitly specified types (thus, a conversion is necessary), e.g.

// error: call of overloaded 'cast<int, float>(unsigned int)' is ambiguous
std::cout << cast<int,float>(10u) << "\n";