Overloading `operator==` for a C++ Class Hierarchy

Recently I needed to define the equality operator between objects in a class hierarchy. A quick search revealed some discussions on this topic, and the opinion appears to be that this, while certainly doable, does not have a clean, elegant solution.

Techniques involved in this task include operator==, virtual functions, API design in a class hierarchy, and the very concept of object equality.

After a few iterations, I’ve settled with a solution. In fact it’s not bad. It’s systematic and routine. The code is listed below; some observations follow.

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#include <cassert>
#include <typeinfo>
#include <typeindex>
#include <iostream>
#include <memory>
#include <string>

using namespace std;


class A
{
    private:
        int _a;

    protected:
        virtual bool _equals(A const & other) const
        {
            if (typeid(*this) != typeid(other)) return false;
            return this->_a == other._a;
        }

    public:
        A(int a) : _a{a} {}

        bool operator==(A const & other) const {
            return this->_equals(other);
        }

        bool operator!=(A const & other) const {
            return !(*this == other);
        }
};


class B : public A
{
    private:
        int _b;

    protected:
        virtual bool _equals(A const & other) const
        {
            if (typeid(*this) != typeid(other)) return false;
            auto that = static_cast<B const &>(other);
            if (this->_b != that._b) return false;
            return A::_equals(other);
        }

    public:
        B(int a, int b) : A(a), _b{b} {}
};


class C : public A
{
    private:
        int _c;

    protected:
        virtual bool _equals(A const & other) const
        {
            if (typeid(*this) != typeid(other)) return false;
            auto that = static_cast<C const &>(other);
            if (this->_c != that._c) return false;
            return A::_equals(other);
        }

    public:
        C(int a, int c): A(a), _c{c} {}
};


class D : public C
{
    private:
        int _d;

    protected:
        virtual bool _equals(A const & other) const
        {
            if (typeid(*this) != typeid(other)) return false;
            auto that = static_cast<D const &>(other);
            if (this->_d != that._d) return false;
            return C::_equals(other);
        }

    public:
        D(int a, int c, int d): C(a, c), _d{d} {}
};


class E: public D
{
    public:
        E(int a, int c, int d) : D(a, c, d) {}
};


class F : public E
{
    private:
        int _f;

    protected:
        virtual bool _equals(A const & other) const
        {
            if (typeid(*this) != typeid(other)) return false;
            auto that = static_cast<F const &>(other);
            if (this->_f != that._f) return false;
            return E::_equals(other);
        }

    public:
        F(int a, int c, int d, int f): E(a, c, d), _f{f} {}
};




int main()
{
    A a1(2);
    A a2(2);
    A a3(3);
    B b1{2, 3};
    B b2{2, 3};
    B b3{3, 3};
    B b4(3, 4);
    C c1{8, 4};
    C c2{8, 4};
    C c3{7, 4};
    C c4{7, 5};
    D d1(1, 2, 3);
    D d2(1, 2, 3);
    D d3(1, 2, 4);
    D d4(2, 2, 4);
    D d5(1, 3, 3);
    F f1(1, 2, 3, 4);
    F f2(1, 2, 3, 4);
    F f3(1, 3, 3, 4);
    F f4(1, 2, 3, 4);

    assert(a1 == a2);
    assert(a2 != a3);
    assert(b1 == b2);
    assert(b1 != b3);
    assert(b3 != b4);
    assert(c1 == c2);
    assert(c1 != c3);
    assert(c3 != c4);
    assert(d1 == d2);
    assert(d1 != d3);
    assert(d3 != d4);
    assert(d1 != d5);
    assert(f1 == f2);
    assert(f2 != f3);
    assert(f3 != f4);

    assert(a1 != b2);
    assert(b3 != a2);
    assert(a2 != c2);
    assert(c3 != a1);
    assert(a2 != d1);
    assert(d5 != a1);
    assert(b2 != c3);
    assert(c3 != b1);
    assert(c4 != d1);
    assert(d3 != c2);
    assert(d2 != f1);
    assert(f2 != c3);

    assert(typeid(a1) == typeid(a2));
    assert(typeid(b1) == typeid(b3));
    assert(typeid(c3) == typeid(c4));
    assert(typeid(d1) == typeid(d4));
    assert(typeid(f1) == typeid(f2));
    assert(typeid(a1) != typeid(b1));
    assert(typeid(b1) != typeid(c1));
    assert(typeid(c1) != typeid(d1));
    assert(typeid(d1) != typeid(f3));

    assert(type_index(typeid(a1)) == type_index(typeid(a3)));
    assert(type_index(typeid(b1)) == type_index(typeid(b3)));
    assert(type_index(typeid(c1)) == type_index(typeid(c3)));
    assert(type_index(typeid(d3)) == type_index(typeid(d4)));
    assert(type_index(typeid(a1)) != type_index(typeid(c1)));

    assert(type_index(typeid(a2)).hash_code() == type_index(typeid(a3)).hash_code());
    assert(type_index(typeid(b1)).hash_code() == type_index(typeid(b3)).hash_code());
    assert(type_index(typeid(c1)).hash_code() == type_index(typeid(c3)).hash_code());
    assert(type_index(typeid(d2)).hash_code() == type_index(typeid(d3)).hash_code());
    assert(type_index(typeid(b2)).hash_code() != type_index(typeid(c2)).hash_code());

    A* aa1 = &a1;
    A* aa2 = &a2;
    A* aa3 = &a3;
    A* ab1 = &b1;
    A* ab2 = &b2;
    A* ab3 = &b3;
    A* ab4 = &b4;
    A* ac1 = &c1;
    A* ac2 = &c2;
    A* ac3 = &c3;
    A* ac4 = &c4;
    A* ad1 = &d1;
    A* ad2 = &d2;
    A* ad3 = &d3;
    A* ad4 = &d4;
    A* ad5 = &d5;
    A* af1 = &f1;
    A* af2 = &f2;
    A* af3 = &f3;
    A* af4 = &f4;

    assert(*aa1 == *aa2);
    assert(*aa2 != *aa3);
    assert(*ab1 == *ab2);
    assert(*ab1 != *ab3);
    assert(*ab3 != *ab4);
    assert(*ac1 == *ac2);
    assert(*ac1 != *ac3);
    assert(*ac3 != *ac4);
    assert(*ad1 == *ad2);
    assert(*ad1 != *ad3);
    assert(*ad3 != *ad4);
    assert(*ad1 != *ad5);
    assert(*af1 == *af2);
    assert(*af2 != *af3);
    assert(*af3 != *af4);

    assert(typeid(*aa1) == typeid(*aa2));
    assert(typeid(*ab1) == typeid(*ab3));
    assert(typeid(*ac3) == typeid(*ac4));
    assert(typeid(*ad1) == typeid(*ad4));
    assert(typeid(*af1) == typeid(*af2));
    assert(typeid(*aa1) != typeid(*ab1));
    assert(typeid(*ab1) != typeid(*ac1));
    assert(typeid(*ac1) != typeid(*ad1));
    assert(typeid(*ad1) != typeid(*af3));

    assert(type_index(typeid(*aa1)) == type_index(typeid(*aa3)));
    assert(type_index(typeid(*ab1)) == type_index(typeid(*ab3)));
    assert(type_index(typeid(*ac1)) == type_index(typeid(*ac3)));
    assert(type_index(typeid(*ad3)) == type_index(typeid(*ad4)));
    assert(type_index(typeid(*aa1)) != type_index(typeid(*ac1)));

    assert(type_index(typeid(*aa2)).hash_code() == type_index(typeid(*aa3)).hash_code());
    assert(type_index(typeid(*ab1)).hash_code() == type_index(typeid(*ab3)).hash_code());
    assert(type_index(typeid(*ac1)).hash_code() == type_index(typeid(*ac3)).hash_code());
    assert(type_index(typeid(*ad2)).hash_code() == type_index(typeid(*ad3)).hash_code());
    assert(type_index(typeid(*ab2)).hash_code() != type_index(typeid(*ac2)).hash_code());

    unique_ptr<A> uaa1(new A(move(a1)));
    unique_ptr<A> uab1(new B(move(b1)));
    unique_ptr<A> uab2(new B(move(b2)));
    unique_ptr<A> uac1(new C(move(c1)));

    assert(*uab1 == *uab2);
    assert(*uaa1 != *uab2);
    assert(*uab1 != *uac1);

    assert(typeid(*uab1) != typeid(*uac1));
    assert(typeid(*uab1) == typeid(*uab2));
}

All the assertions in this code should pass.

We see the solution is quite systematic and routine. The pattern is clear:

  • The root class defines a public function for operator==, which sets the API. This function is inherited by every subclass and I didn’t see a need to overide or customize this function in any subclass. This function calls a protected virtual function called _equals (of course one can replace this name with whatever they prefer). It’s often useful to define a operator!= which simply negates the result of operator==.
  • Every subclass that has its own data members that affect the equality relation of two objects of that subclass should re-define _equals, and keep it protected and virtual.
  • All the operator==, operator!=, and _quals functions have a single argument which is a const reference to the root class, not any particular subclass.
  • The function _equals does exactly three things:
    1. Check for un-equality according to typeid, which determines the dynamic type of both the ‘current’ and the ‘other’ objects.
    2. Check for un-equality according to data members, if any, introduced in the ‘current’ subclass (meaning the subclass in which the the implementation of _equals is in question).
    3. Call _equals of the parent class (unless the current class is the root class).

Why does the solution take this route?

First, I’ve used a public, non-virtual operator== to define the API, and delegated implementation details to a protected virtual function _equals. This follows Herb Sutter’s recommendations.

Second, the public API defines the comparison between any two objects in the class hierarchy, on both sides of the == sign.

Third, why do we need to check typeid? Clearly, the typeids of both objects must match in order for them to be equal. But can we omit this check and achieve the same effect? Suppose this is an object of class C and other is an object of class D (a subclass of C), then C::_equals is called. When other is cast to an object of class C, any data members of other that are introduced in class D are lost. As long as the C and A parts of other match those of this, the function will return true. This is of course the wrong answer, because the D-specific extra stuff in other do not participate in the comparison, as they should.

On the other hand, suppose this is a D object and other is a C object, then D::_equals is called. If we omit the check on typeid and go ahead cast other to class D (of subclass of C), it will be a run-time (or compile-time?) error.

Fourth, the rational for comparison based on data members of the this class is easy to understand. Actually, after the typeid check and cast, both this and other are of the same class, as they actually are but possibly disguised by the declared type of the references. Only when the object other is treated as exactly its dynamic type, not any base class (whereas other can’t be of a subclass of the class of this, given that it has passed the typeid check), can we fully access all the data members defined in this class of this, and define equality based on this data members however we like.

Fifth, why is the call to the parent’s _equals? Well, if not, then data members of this and other that are defined in ‘upstream’ classes do not affect the determination of equality, which is wrong.

Sixth, why is _equals kept protected and virtual throughout? It needs to be protected, rather than private, because it needs to be called by subclasses. It needs to be virtual, even in a ‘leaf’ class, because any class in this hierarchy may be subclassed later either in our own code or in user’s separate code, and in that situation we need polymorphism to remain functional.

[Correction]

In April 2024, Jeremy Overesch pointed out an issue:

In the `_equals` functions, there is a line similar to the following, which I believe is incorrectly doing a copy:

auto that = static_cast<B const &>(other);

Unfortunately, auto by default does a copy. In order to do a reference, it needs to be explicit:

auto& that = static_cast<B const &>(other);

Thanks, Jeremy!

Written on January 27, 2018