I'm designing a little mathematical library. I have classes that represents classes of function, e.g. polynomial. When they're instantiated, the parameters needed (a1, a2, a3) are provided so the object actually represent a specific polynomial (a1*x^2 + a2*x + a3).
Then I want to provide the functionality of evaluating the function at a certain point (x=3, y=?). I've read this wiki and chapter 12 of Thinking in C++, Vol. 1 by Bruce Eckel. Both of them says that I should decide whether to overload or not based on the "meaning" of the operator. I'm not an experienced C++ programmer, but to my knowledge, if I have a class representing a function and I use obj(x) what I expect is the value y the function takes at that x.
The doubts arises with dimensions: I have to represent vector functions too (http://en.wikipedia.org/wiki/Vector_function), like a1*x1 + a2*x2, and I will have signature like this: operator()(real x1, real x2). My problem is with the return type. If y1 = a1*x1 + a2*x2 is a vector (both mathematically and in C++), should I return y1 by value or by reference? And should I provide also a const version?
PS it's my first question here on Stackoverflow.com so please tell me if something of the question is wrong (title, tags, question itself :P) and I'll gladly correct it.
'should I return y1 by value or by reference?' By value undoubtedly, there's no good way to return a reference to a newly created object. If the cost of copying your objects is an issue then you should look to some kind of smart pointer technique to provide fast copying.
'And should I provide also a const version?' From what you have said you should only provide a const version.