Operator overloading : member function vs. non-member function?

Question

I read that an overloaded operator declared as member function is asymmetric because it can have only one parameter and the other parameter passed automatically is

Answer 1

If you define your operator overloaded function as member function, then the compiler translates expressions like s1 + s2 into s1.operator+(s2). That means, the operator overloaded member function gets invoked on the first operand. That is how member functions work!

But what if the first operand is not a class? There's a major problem if we want to overload an operator where the first operand is not a class type, rather say double. So you cannot write like this 10.0 + s2. However, you can write operator overloaded member function for expressions like s1 + 10.0.

To solve this ordering problem, we define operator overloaded function as friend IF it needs to access private members. Make it friend ONLY when it needs to access private members. Otherwise simply make it non-friend non-member function to improve encapsulation!

class Sample
{
 public:
    Sample operator + (const Sample& op2); //works with s1 + s2
    Sample operator + (double op2); //works with s1 + 10.0

   //Make it `friend` only when it needs to access private members. 
   //Otherwise simply make it **non-friend non-member** function.
    friend Sample operator + (double op1, const Sample& op2); //works with 10.0 + s2
}

Read these :
A slight problem of ordering in operands
How Non-Member Functions Improve Encapsulation

Answer 2

It's not necessarily a distinction between friend operator overloads and member function operator overloads as it is between global operator overloads and member function operator overloads.

One reason to prefer a global operator overload is if you want to allow expressions where the class type appears on the right hand side of a binary operator. For example:

Foo f = 100;
int x = 10;
cout << x + f;

This only works if there is a global operator overload for

Foo operator + (int x, const Foo& f);

Note that the global operator overload doesn't necessarily need to be a friend function. This is only necessary if it needs access to private members of Foo, but that is not always the case.

Regardless, if Foo only had a member function operator overload, like:

class Foo
{
  ...
  Foo operator + (int x);
  ...
};

...then we would only be able to have expressions where a Foo instance appears on the left of the plus operator.