oop - C++ Double Dispatch for Equals()

Question

Imagine I have abstract base class Shape, with derived classes Circle and Rectangle.

class Shape {};
class Circle : public Shape {};
class Rectangle : public Shape {};

I need to determine if two shapes are equal, assuming I have two Shape* pointers. (This is because I have two instances of vector<Shape*> and I want to see if they have the same shapes.)

The recommended way to do this is double dispatch. What I've come up with is this (greatly simplified here, so that shapes are equal to all other shapes of the same type):

class Shape {
public:
    virtual bool equals(Shape* other_shape) = 0;
protected:
    virtual bool is_equal(Circle& circle) { return false; };
    virtual bool is_equal(Rectangle& rect) { return false; };
    friend class Circle;    // so Rectangle::equals can access Circle::is_equal
    friend class Rectangle; // and vice versa
};

class Circle : public Shape {
public:
    virtual bool equals(Shape* other_shape) { return other_shape->is_equal(*this); };
protected:
    virtual bool is_equal(Circle& circle) { return true; };
};

class Rectangle : public Shape {
public:
    virtual bool equals(Shape* other_shape) { return other_shape->is_equal(*this); };
protected:
    virtual bool is_equal(Rectangle& circle) { return true; };
};

This works, but I have to add a separate equals function and friend declaration in Shape for each derived class. Then I have to copy-paste the exact same equals function into each derived class, too. This is an awful lot of boilerplate for say, 10 different shapes!

Is there a simpler way to do it?

dynamic_cast is out of the question; too slow. (Yes, I benchmarked it. Speed matters in my app.)

I tried this but it doesn't work:

class Shape {
public:
    virtual bool equals(Shape* other_shape) = 0;
private:
    virtual bool is_equal(Shape& circle) { return false; };
};

class Circle : public Shape {
public:
    virtual bool equals(Shape* other_shape) { return other_shape->is_equal(*this); };
private:
    virtual bool is_equal(Circle& circle) { return true; };
};

class Rectangle : public Shape {
public:
    virtual bool equals(Shape* other_shape) { return other_shape->is_equal(*this); };
private:
    virtual bool is_equal(Rectangle& circle) { return true; };
};

equals() always returns false, even on identical shapes. It seems dispatch is always choosing the is_equal(Shape&) base function, even when a "more specific" match is available. This probably makes sense but I don't understand C++ dispatch well enough to know why.

Answer 1

Double-dispatch has been well studied. The generalization of double-dispatch is called a "multi-method".

Chapter 11 of Modern C++ Design addresses this issue in detail. The approach using dynamic_cast<> that you described is in section 11.3 "Double Switch-on-Type: Brute Force". The author even describes how to automate most of the work and automatically generate the symmetric overloads. Then, the author introduces a logarithmic dispatch based on std::map<> and std::type_info. Finally, the section ends with "Constant-Time Multimethods: Raw Speed" that's (roughly) based on a matrix of callback functions.

The presented solution includes lengthy explanations on handling functors and casts to avoid nasty pitfalls in presence of multiple (and virtual) inheritance.

If you consider implementing multi-methods in C++, I stronly recommend that you read the book and implement the proposed solution.