C++ create aliases for primitive types using templates?

I'm trying to write some stuff to wrap simd intrinsics, and I figured that it would be nice to do something like

using vec<float, 4> = __m128;

so that I could use templates in some code I write later on. This isn't really relevant to the question, but __m128 is a type that represents 4 floats. This doesn't work, and g++ says expected nested-name-specifier before 'vec'. I know I can just write classes to wrap them, or I can do something like:

template <typename T, int N> struct vec;

template<> struct vec<float, 4>
{
    typedef __m128 type;
};

and then I can use vec<float,4>::type, but the first way is far more convenient. I think it might be possible using something like C++ template typedef, but I'm not sure, and I wouldn't know the syntax. Is there any way to make the first statement work or to do something similar?