Strong exception safety guaranty - Did I forget something ?

Hello all,

[All code in this post is here only for illustration and may not compile
as is]

I'm writing a class with value semantic, and I want its public interface
to provide the strong exception safety guaranty (if a public operation
fails for any reason, then an exception is thrown, and the object is
left in its previous state)

My class's data members are standard containers and built-in types. For
the question, let's assume

typedef std::vector< int > vect;

class my_class
{
public:
     my_class();
     // ~my_class(); // Default implementation ok
     // my_class( const my_class& ); // Default implementation ok
     my_class& operator=( const my_class& );
public:
     void modify();
private:
     vect compute_modified_vect();
private:
     bool my_bool;
     vect my_vect;
};

vect my_class::compute_modified_vect()
{
     vect new_vect;
     // No special care about exception safety
     // while modifying new_vect
     return new_vect;
}

void my_class::modify()
{
     compute_modified_vect().swap( my_vect );
     m_bool = true;
}

my_class& my_class::operator=( const my_class& i )
{
     vect new_vect( i.my_vect );
     new_vect.swap( my_vect );
     my_bool = i.my_bool;
     return *this;
}

*The questions*
1) Do I really have to write operator= ? As far as I know, the default
copy assignment operator gives no guaranty about exception safety, but I
may have missed something.

2) Is my implementation of operator= correct ?

3) Since I thought very late in my conception that I may have to write
operator=, I wonder if there are other operations that I should write.

4) Is my implementation of my_class::modify correct ?

5) Any other suggestion/comment ?

Many thanks,
--
Vincent Jacques

"S'il n'y a pas de solution, c'est qu'il n'y a pas de probl?me"
                 Devise Shadock