Perhaps your problem has nothing to do with computing the vector half-way between two other vectors.

I suggest you set up a very simple situation so instead of "the results don't look correct", you can actually get a specific call to this code that doesn't do the right thing. Then fire up the debugger and see where it's going wrong.

For instance (make a picture ignoring the coordinate z to follow along), if you look from the origin along (1,0,0) at a sphere with center (3,-1,0) and radius sqrt(2), you will hit it at (2,0,0). At that point the normal to the sphere is (-sqrt(0.5),sqrt(0.5),0). If you put a light source at (2,10,0), you should be smack in the middle of the specular highlight. What does your code do in that case?

You should not add a diffuse or specular contribution if the dot product between the normal and the direction to the light is negative (you have "fabs" in there, which creates the artifact in the middle part of the sphere on the first picture).

EDIT: Wikipedia seems to agree:

Although the above formulation is the common way of presenting the Phong reflection model, each term should only be included if the term's dot product is positive. (Additionally, the specular term should only be included if the dot product of the diffuse term is positive.)[/quote]

If you put the light above the object, or perhaps a little bit behind the camera, you'll get a better view of the specular highlight and you'll have a better idea of whether it looks right.