Should comparison be implemented under `compare` or `operator ==` when both are needed?

Question

In making a class, the compare method and the operator== overload should have identical functionality. Therefore, only one implementation is needed, and I'm trying to figure out if there's any reason why it should be defined in the compare method rather than the operator== overload.

Here's the structure defining comparison in compare:

class T {
// definition of field f
...
   bool compare(const T& t) const {
      if (this->f == t.f) { return true; }
      return false;
   }

   friend bool operator == (const T& lhs, const T& rhs) { return lhs.compare(rhs); }
}

versus in the operator == overloading:

class T {
// definition of field f
...
   bool compare(const T& t) const { return *this == t; }

   friend bool operator == (const T& lhs, const T& rhs) {
      if (lhs.f == t.f) { return true; }
      return false;
   }
}

Answer 1

TL;DR use second variant with 'virtual' keyword, but it will be better to get rid of this bullshit at all and use operator== only

You should use method compare() only if you have other variant of objects comparison, otherwise it does not make any sense. The reason for this is implementation of std::map, std::set, sorting alghoritms, etc., which use operator==, so if you use first variation of == implementation it will be, basicaly, your operator==, but with other name, which does not make any sense. If you still want to do it,

-You can use first variant(where == uses compare), but make compare method virtual. In this case you will be able to overload comparison method just like in Java and it will affect on comparison, but still you can do it just by creating operator== for children class, so it still doesn't make any sense

...or you can use second one, but still using 'virtual' keyword to change implementation of parent class in children classes and if you don't like == implementation you can use compare method

Not very relatable example, but I think it might help you. In OpenCV library assignment operator= for class Mat(this class contains literally array of pixels and nothing more) don't actually copies array, but copies only a pointer on array of pixels(because it's heavy operation and it doesn't required in many cases), and for actual copying method clone() used. I think you can use the same solution for your code