Template Class Member Function Only Specialization

explicit specialization of template class member function

It doesn't work that way. You would need to say the following, but it is not correct

template <class C> template<>
void X<C>::get_as<double>()
{

}

Explicitly specialized members need their surrounding class templates to be explicitly specialized as well. So you need to say the following, which would only specialize the member for X<int>.

template <> template<>
void X<int>::get_as<double>()
{

}

If you want to keep the surrounding template unspecialized, you have several choices. I prefer overloads

template <class C> class X
{
   template<typename T> struct type { };

public:
   template <class T> void get_as() {
     get_as(type<T>());
   }

private:
   template<typename T> void get_as(type<T>) {

   }

   void get_as(type<double>) {

   }
};

Template member function specialization in a template class

Why does this member function specialization get error?

When you instantiate the template class A for example A<std::vector<int>>, the template parameter T is equal to std::vector<int>, not std::vector<T>, and this a specialization case of the function. Unfortunately this can not be done with member functions as mentioned in the comments.

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Are there some better solutions?

Yes; In c++17 you could use if constexpr with a trait to check the std::vector, like this.

#include <type_traits> // std::false_type, std::true_type
#include <vector>

// traits for checking wether T is a type of std::vector<>
template<typename T> struct is_std_vector final : std::false_type {};
template<typename... T> struct is_std_vector<std::vector<T...>> final : std::true_type {};

template<typename T>
class A /* final */
{
    T mData;

public:  
    // ...constructor  

    void print() const /* noexcept */
    {
        if constexpr (is_std_vector<T>::value) // when T == `std::vector<>`
        {
            for (const auto element : mData)
                std::cout << element << "\n";
        }
        else // for types other than `std::vector<>` 
        {
            std::cout << mData << std::endl;
        }
    }
};

(See Live Online)

This way you keep only one template class and the print() will instantiate the appropriate part according to the template type T at compile time.

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If you don not have access to C++17, other option is to SFINAE the members(Since c++11).

#include <type_traits> // std::false_type, std::true_type, std::enbale_if
#include <vector>

// traits for checking wether T is a type of std::vector<>
template<typename T> struct is_std_vector final : std::false_type {};
template<typename... T> struct is_std_vector<std::vector<T...>> final : std::true_type {};

template<typename T>
class A /* final */
{
    T mData;

public:  
    // ...constructor  

    template<typename Type = T> // when T == `std::vector<>`
    auto print() const -> typename std::enable_if<is_std_vector<Type>::value>::type
    {
        for (const auto element : mData)
                std::cout << element << "\n";
    }

    template<typename Type = T> // for types other than `std::vector<>`
    auto print() const -> typename std::enable_if<!is_std_vector<Type>::value>::type
    {
        std::cout << mData << std::endl;
    }
};

(See Live Online)

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What if I have more other data types like self-define vector classes
or matrices? Do I have to define many is_xx_vector?

You can check the type is a specialization of the provided one like as follows. This way you can avoid providing many traits for each type. The is_specialization is basically inspired from this post

#include <type_traits> // std::false_type, std::true_type
#include <vector>

// custom MyVector (An example)
template<typename T> struct MyVector {};

template<typename Test, template<typename...> class ClassType>
struct is_specialization final : std::false_type {};

template<template<typename...> class ClassType, typename... Args>
struct is_specialization<ClassType<Args...>, ClassType> final : std::true_type {};

And the print function could be in c++17:

void print() const /* noexcept */
{
   if constexpr (is_specialization<T, std::vector>::value)// when T == `std::vector<>`
   {
      for (const auto element : mData)
         std::cout << element << "\n";
   }
   else if constexpr (is_specialization<T, ::MyVector>::value)  // custom `MyVector`
   {
      std::cout << "MyVector\n";
   }
   else  // for types other than `std::vector<>` and custom `MyVector`
   {
      std::cout << mData << std::endl;
   }
}

(See Live Online)

template class member function only specialization

I think it is referring to the following case:

template <typename T>
struct base {
   void foo() { std::cout << "generic" << std::endl; }
   void bar() { std::cout << "bar" << std::endl; }
};
template <>
void base<int>::foo() // specialize only one member
{ 
   std::cout << "int" << std::endl; 
}
int main() {
   base<int> i;
   i.foo();         // int
   i.bar();         // bar
}

Once that is done, you cannot specialize the full template to be any other thing, so

template <>
struct base<int> {};  // error

Template member function specialization of a templated class without specifying the class template parameter

You can use a technique called tag dispatch and replace the template specialisations by function overloads.

template<typename>
struct Tag {};

template <class A>
struct C3
{
 void f_impl(Tag<int>) const;
 void f_impl(Tag<char>) const;
 template<class B>
 void f() const {
     f_impl(Tag<B>{});
 }
};

struct D { static int g(void){ return 999; } };

template <class A>
void C3<A>::f_impl(Tag<int>) const { std::cout<<A::g()+1<<std::endl; }

template <class A>
void C3<A>::f_impl(Tag<char>) const { std::cout<<A::g()+2<<std::endl; }

Then your call site looks exactly as you want:

 C3<D> c3; c3.f<int>();  // expect to see 1000
 C3<D> c4; c4.f<char>(); // expect to see 1001

Full example here.

Adding Member Function to only Specialized Template of Class

You can factor the common code in a base class template and make derived specialization with the tailored features.

template <typename T>
class BaseMatch { /* Common features across all specializations... */ };

template <typename T>
class Match : BaseMatch<T> { /* Generic case, no custom behavior to enforce */ };

template <>
class Match<std::string> : BaseMatch<std::string> {
    void string_function() { /* ... */ }
};

template class - member function specialization

Not compliantly, it doesn't.

FWIW, GCC 4.8 rejects your code without the template <>.

Your compiler is either buggy or has an extension to support this; I can confirm that MSVS 2012 accepts the code. I'm told that MSVS 2013 November CTP also eats it up without complaint. To be fair, Visual Studio was always fairly lenient about template specifications.

[C++11: 14.7/3]: An explicit specialization may be declared for a function template, a class template, a member of a class template or a member template. An explicit specialization declaration is introduced by template<>. [..]

The only exception to this rule is:

[C++11: 14.7.3/5]: [..] Members of an explicitly specialized class template are
defined in the same manner as members of normal classes, and not using the template<> syntax. [..]

… but that does not apply here.

How to specialize template member function?

As Igor mentioned, you can implement the generic version in the header file, and then the specialization in the cpp file, for example:

// MyStruct.h

struct MyStruct {
  // ...
  template <typename T>
  void readField(std::istream& in, T& data) {
    read(in, data);
    data = ntohl(data);
  }
};

Then in the cpp file you can implement the specialization, for example:

// MyStruct.cpp

template <>
void MyStruct::readField<uint8_t>(std::istream& in, uint8_t& data) {
  read(in, data);
}

Update: After reading the comments, the specialization can also be in the same header file as the primary template, but not within the struct, for example (I verified this by compiling and running a similar example without error):

// MyStruct.h

struct MyStruct {
  // ...
  template <typename T>
  void readField(std::istream& in, T& data) {
    read(in, data);
    data = ntohl(data);
  }
};  

template <>
inline void MyStruct::readField<uint8_t>(std::istream& in, uint8_t& data) {
  read(in, data);
}

// End MyStruct.h

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