Return type based on value of input parameter

Question

In C++11 is there a way to implement a sqrt function that works for both positive and negative double input values? I would like the return type to be std::complex<double> if the input is negative and a double if it is positive. I realize the simple solution is to just always return std::complex<double> but this is not what I am looking for.

Below I have an example of my first attempt, however this does not compile due to the presence of a in the return type:

inline decltype((a > 0)?(double):(std::complex<double>)) sqrt(const double& a)
{
    if(a > 0)
    {
        return std::sqrt(a);
    }
    else
    {
        return ((std::complex<double>(0.0,1.0))*std::sqrt(-a));
    }
}

Answer 1

No, this is not possible.

Types are compile-time constructs, and your function's type is fixed at compile-time.

Were the argument provided as a constexpr "constant expression", then you might have used templates to solve your problem. But, with dynamic inputs, this is simply not possible.

Answer 2

You could return a boost::variant<double, std::complex<double>> (since the decision has to be made at runtime), but that seems like adding a lot of complexity to your code for no real gain.

Answer 3

It's not possible, and probably more importantly, probably wouldn't be useful even if you could do it.

Since the function can return a complex number, the calling code needs to be prepared to process a complex number. If your code needs to be able to process complex numbers in any case, it almost certainly makes more sense to always return a complex number, and if the input was positive it'll be of the form X + 0i (i.e., the imaginary part will equal 0).

In theory, you could do this in a language that supported dynamic typing -- but even with most of them, sqrt is basically statically typed. If the input you provide is a real number, the result will also be a real number, and if the input was negative the result will typically be a NaN or something on that order. If (and only if) you provide the input as a complex number will you receive a complex number as the result.