Why are function template specializations not allo

After having found answers to many of my questions on stackoverflow, I have now come up against a question of which I can't find the answer and I hope that someone is willing to help me!

My problem is that I want to do an explicit templatization of a function inside a class in C++. My compiler (g++) and a look in the C++ standard (§14.7.3) tells me that this specialization has to be done in the namespace in which the class is declared. I understand that this implies that I cannot put the specialization inside the class, but I don't see the point of this restriction! Does anyone know if there is a good reason for not letting the specializations be made inside the class?

I know that there are workarounds, e.g. to put the function inside a struct, but I want to understand why the language has this design. If there is a good reason for not allowing specialized functions inside the class, I guess I should know it before trying to work around it.

Thanks in advance!

To make my question a little bit more precise: Here is some code from a test example which illustrates what I want to do:

#include <cstdio>

namespace MalinTester {

template <size_t DIMENSIONALITY>
class SpecializationTest {
public:
    SpecializationTest() {
        privateVariable = 5;
    };
    virtual ~SpecializationTest() {};

    void execute() {
        execute<DIMENSIONALITY>();
    };

private:
    int privateVariable;
    template <size_t currentDim>
    static void execute() {
        printf("This is the general case. Current dim is %d. The private variable is %d.\n", currentDim, privateVariable);
        execute<currentDim-1>();
    }

    template <>
    static void execute<0>() {
        printf("This is the base case. Current dim is 0.\n");
    }

};

This is not possible; g++ says:

SpecializationTest_fcn.h:27: error: explicit specialization in non-namespace scope ‘class MalinTester::SpecializationTest<DIMENSIONALITY>’
SpecializationTest_fcn.h:28: error: template-id ‘execute<0>’ in declaration of primary template

If I put the function execute outside the class, in the name space MalinTester, it will look like this:

#include <cstdio>

namespace MalinTester {

    template <size_t DIMENSIONALITY> class SpecializationTest {};

    template <size_t currentDim>
    void execute() {
        printf("This is the general case. Current dim is %d. The private variable is %d.\n", currentDim, privateVariable);
        execute<currentDim-1>();
    }

    template <>
    void execute<0>() {
        printf("This is the base case. Current dim is 0.\n");
    }

    template <size_t DIMENSIONALITY>
    class SpecializationTest {
    public:
        SpecializationTest() {};
        virtual ~SpecializationTest() {};

        void execute() {
            MalinTester::execute<DIMENSIONALITY>();
        };
    private:
        int privateVariable = 5;
    };
};
};

and I cannot use privatevariable in the templatized versions of execute, as it is private in the class. I really want it private, as I want to have my data encapsulated as far as possible.

Of course I can send privateVariable as an argument to the function, but I think it would be more beautiful to avoid this, and what I really wonder is if there is a good reason for the C++ standard not to allow explicit specialization as in the first code example above.

@Arne Mertz: This is the workaround I have tried, but it doesn't allow using privateVariable either. And most of all, I wonder if it is a good idea to do like this. As I'm not allowed to make specializations of member functions, maybe I shouldn't do specializations of functions encapsulated in structs inside the class either.

#include <cstdio>

namespace MalinTester {

template <size_t DIMENSIONALITY>
class SpecializationTest {
public:
    SpecializationTest() {
        privateVariable = 5;
    };
    virtual ~SpecializationTest() {};

    void execute() {
        Loop<DIMENSIONALITY, 0>::execute();
    };

private:
    int privateVariable;

    template <size_t currentDim, size_t DUMMY>
    struct Loop {
        static void execute() {
            printf("This is the general case. Current dim is %d.\n", currentDim);
            Loop<currentDim-1, 0>::execute();
        }
    };

    template <size_t DUMMY>
    struct Loop<0, DUMMY> {
        static void execute() {
            printf("This is the base case. Current dim is 0.\n");
        }
    };
};
};

Base specialization:

In .h:

template <class T>
class UISelectorSlider :  public UISelectorFromRange<T> {
public:
    UISelectorSlider();
    virtual ~UISelectorSlider();
private:
    float width;
    float getPositionFromValue(T value);
};

In .cpp under same namespace:

template <>
float UISelectorSlider<MVHue>::getPositionFromValue(MVHue value)
{
    return width * (float)value / 360.0;
}

If you want specialized function within specialized class:

Inside class add (.h) (private function):

private:
    template <int I>
    void foo();

Specialization inside .cpp:

template <>
template <>
void UISelectorSlider<MVHue>::foo<3>()
{
     // you can access private fields here
}

UPDATE:

But you cant write something like this:

template <class T>
template <>
void UISelectorSlider<T>::foo<3>()
{
     // you can access private fields here
}

You will get: error: enclosing class templates are not explicitly specialized.

It does not matter is this definition inside class or in namespace. The point is that this is not exact partial specialization - this function does not have defined context class (which members you want to call). In other words - when you specialize member you actually try specialize the whole containing class, but not the member itself. And compiler cant do that because class is not yet defined completely. So this is restriction by template design. And if it actually worked - templates would be full equivalent to simple macros. (And you probably can will solve your task with some macro magic.)