Pointer to function members: what does `R(*C::*)(Args...)` mean?

Question

Consider the following code:

template <class>
struct test: std::integral_constant<int, 0> {};
template<class R, class C, class... Args>
struct test<R(C::*)(Args...)>: std::integral_constant<int, 1> {};
template<class R, class C, class... Args>
struct test<R(*C::*)(Args...)>: std::integral_constant<int, 2> {};
template<class R, class C, class... Args>
struct test<R(**C::*)(Args...)>: std::integral_constant<int, 3> {};
template<class R, class C, class... Args>
struct test<R(C::**)(Args...)>: std::integral_constant<int, 4> {};
template<class R, class C, class... Args>
struct test<R(C::***)(Args...)>: std::integral_constant<int, 5> {};

I have absolutely no idea of what (*C::*), (**C::*), (C::**) and (C::***) mean. I would like an example of a test<decltype(f)> whose value would be equal to 2, 3, 4 and 5. Plus, in that case, how is the syntax for f that would call the member function?

Answer 1

Consider this example:

struct s {
    void test1();
    void(*test2)();
    void(**test3)();
};

int main() {
    static_assert(test<decltype(&s::test1)>::value == 1);   
    static_assert(test<decltype(&s::test2)>::value == 2);   
    static_assert(test<decltype(&s::test3)>::value == 3);   

    auto test4 = &s::test1;
    static_assert(test<decltype(&test4)>::value == 4);   

    auto test5 = &test4;
    static_assert(test<decltype(&test5)>::value == 5);   
}

Here are the types:

R(C::*)(Args...) - A pointer to a member function.
R(*C::*)(Args...) - A pointer to a data member that is a function pointer.
R(**C::*)(Args...) - A pointer to a data member that is a pointer to a function pointer.
R(C::**)(Args...) - A pointer to a pointer to a member function.
R(C::***)(Args...) - A pointer to a pointer to a pointer to a member function.

To call these, consider a slightly modified example:

struct s {
    void test1() {std::cout << "test1\n";}
    void(*test2)() = [] {std::cout << "test2\n";};

    void(*test3Helper)() = [] {std::cout << "test3\n";};
    void(**test3)() = &test3Helper;

    void test4() {std::cout << "test4\n";}
    void test5() {std::cout << "test5\n";}
};

int main() {
    s obj;  

    auto test4 = &s::test4;

    auto test5Helper = &s::test5;
    auto test5 = &test5Helper;  

    (obj.*(&s::test1))();
    (*(obj.*(&s::test2)))(); // note that the dereference is unnecessary
    (**(obj.*(&s::test3)))(); // note that the second dereference is unnecessary
    (obj.**(&test4))();
    (obj.***(&test5))();
}

Note that in each case, if you have a variable with the value of the appropriate &[s::]testN, you can replace (&[s::]testN) with that variable. Note also that for test2 and test3, I dereferenced until getting the function back rather than the function pointer for illustration purposes.