When are stateless class functors useful in place of a c style function?

Question

I've found some good examples of functors on SO like this one, and all the convincing examples seem to use state in the class that defines operator().

I came across an example in a book that defines the function call operator without having state, and I can't help but feel like this is an awkward usage, and that a normal style function pointer, would be better than using operator() in every way here - less code, less variables (you have to instantiate the comparators), its probably more efficient due to the instantiation, and no loss of meaning or encapsulation (since it's just one function).

I know std::sort lets you pick between operator() classes and functions, but I've always just used the functions because of the above logic.

What are the reasons why a class might be preferred?

Here's the example (paraphrased):

class Point2D {
   //.. accessors, constructors
   int x,y;
};
class HorizComp {
public:
   bool operator()(const Point2D& p, const Point2D& q) const
   { return p.getX() < q.getX(); }
};

class VertComp {
public:
   bool operator()(const Point2D& p, const Point2D& q) const
   { return p.getY() < q.getY(); }
};

template <typename E, typename C>
void printSmaller(const E& p, const E& q, const C& isLess) {
   cout << (isLess(p, q) ? p : q) << endl; // print the smaller of p and q
}
//...
// usage in some function:
Point2D p(1.2, 3.2), q(1.5, 9.2);
HorizComp horizComp;
VertComp vorizComp;
printSmaller(p, q, horizComp);
printSmaller(p, q, vorizComp);

Answer 1

The typical reason is that when you do this:

bool less_than(const Point&, const Point&);
// ...
std::sort(..., &less_than);

The template argument for the predicate is the following:

bool(const Point&,const Point&)

Since the sort function receives a function pointer, it is more difficult for the compiler to inline the predicate use inside std::sort(). This happens because you could have another function

bool greater_than(const Point&, const Point&);

which has the exact same type, meaning the std::sort() instatiation would be shared between the two predicates. (remember that I said that it makes inlining more difficult, not impossible).

In contrast, when you do this:

struct less_than {
    bool operator()(const Point&, const Point&) const;
};
// ...
std::sort(..., less_than());


struct greater_than {
    bool operator()(const Point&, const Point&) const;
};
// ...
std::sort(..., greater_than());

The compiler generates a unique template instantiation for std::sort() for each predicate, making it easier to inline the predicate's definition.

Answer 2

One reason is run-time efficiency. If you pass a pointer to a function, the compiler has to be unusually clever to produce code for that function inline. Passing an object that defines operator() makes it much easier for the compiler to produce the code inline. Especially for something like sorting, this can increase speed quite substantially.

In C++11, another reason to use a class is for convenience -- you can use a lambda expression to define the class.