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It is not clear to me of a facet belongs exclusively to one of the four types. 
I have read https://doc.cgal.org/latest/Alpha_shapes_3/index.html#Alpha_shapes_3Definitions and section 2.3 of it. From that it appears it should be exclusive. 
However the sum of number of diffrent types is not eqaul to the number when no condtion is used. I modified the code below and executed it 5 times, four times for each type and then once without the "if" condition so that all facets are counted. 
​​​​​​ Do I need to use infinite precesion for exact match?

Component 1 , general mode
Exterior	7208	ALL	67754
Interior	56668
	63876	diff	3878
Regular	3872
Singular	5450
	9322

  double alpha = 0;
    Alpha_shape_3 as(points.begin(), points.end(), alpha, mode);
    Alpha_iterator opt = as.find_optimal_alpha(num_of_components);
    as.set_alpha(*opt);
    Classification_type in_class_type = Classification_type::SINGULAR;
    for (auto it = as.finite_facets_begin();
        it != as.finite_facets_end();
        it++)
    {
        auto class_type  = as.classify(*it);
        if (in_class_type == class_type)
        {