How partial template specialization chosen?

Question

Please explain me the rules for template specialization selection. I have an example:

template<typename T1, typename T2 = int>
struct S : false_type{};

template<typename T>
struct S<T, float> : true_type{};

cout << boolalpha << S<float>::value;

Why the output is false? And in general, what happens with default template parameter typename T2 = int in specialized classes? Does it introduces some influence?

Answer 1

Choosing a template specialization happens in five steps:

1. Take the primary template declaration. (<T1, T2 = int> S)
2. Fill in user-specified template arguments. (T1 <- float)
3. Function templates only: Deduce additional template arguments.
4. Use defaults for remaining template arguments. (T2 <- int)
5. Use the partial ordering algorithm (C++14 14.5.6.2) to choose the best-matching specialization. (<float, int> does not match <T, float>, so ignore the specialization; only possibility left is primary template)