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Thinking in C++
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One of the most convenient reasons to use global overloaded operators instead of member operators is that in the global versions, automatic type conversion may be applied to either operand, whereas with member objects, the left-hand operand must already be the proper type. If you want both operands to be converted, the global versions can save a lot of coding. Here’s a small example:

//: C12:ReflexivityInOverloading.cpp
class Number {
  int i;
  Number(int ii = 0) : i(ii) {}
  const Number
  operator+(const Number& n) const {
    return Number(i + n.i);
  friend const Number
    operator-(const Number&, const Number&);

const Number
  operator-(const Number& n1,
            const Number& n2) {
    return Number(n1.i - n2.i);

int main() {
  Number a(47), b(11);
  a + b; // OK
  a + 1; // 2nd arg converted to Number
//! 1 + a; // Wrong! 1st arg not of type Number
  a - b; // OK
  a - 1; // 2nd arg converted to Number
  1 - a; // 1st arg converted to Number
} ///:~

Class Number has both a member operator+ and a friend operator–. Because there’s a constructor that takes a single int argument, an int can be automatically converted to a Number, but only under the right conditions. In main( ), you can see that adding a Number to another Number works fine because it’s an exact match to the overloaded operator. Also, when the compiler sees a Number followed by a + and an int, it can match to the member function Number::operator+ and convert the int argument to a Number using the constructor. But when it sees an int, a +, and a Number, it doesn’t know what to do because all it has is Number::operator+, which requires that the left operand already be a Number object. Thus, the compiler issues an error.

With the friend operator–, things are different. The compiler needs to fill in both its arguments however it can; it isn’t restricted to having a Number as the left-hand argument. Thus, if it sees

1 – a

it can convert the first argument to a Number using the constructor.

Sometimes you want to be able to restrict the use of your operators by making them members. For example, when multiplying a matrix by a vector, the vector must go on the right. But if you want your operators to be able to convert either argument, make the operator a friend function.

Fortunately, the compiler will not take 1 – 1 and convert both arguments to Number objects and then call operator–. That would mean that existing C code might suddenly start to work differently. The compiler matches the “simplest” possibility first, which is the built-in operator for the expression 1 – 1.

Thinking in C++
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   Reproduced courtesy of Bruce Eckel, MindView, Inc. Design by Interspire