math - Why does C++ mandate that complex only be instantiated for float, double, or long double?

Question

According to the C++ ISO spec, §26.2/2:

The effect of instantiating the template complex for any type other than float, double or long double is unspecified.

Why would the standard authors explicitly add this restriction? This makes it unspecified, for example, what happens if you make complex<int> or a complex<MyCustomFixedPointType> and seems like an artificial restriction.

Is there a reason for this limitation? Is there a workaround if you want to instantiate complex with your own custom type?

I'm primarily asking this question because of this earlier question, in which the OP was confused as to why abs was giving bizarre outputs for complex<int>. That said, this still doesn't quite make sense given that we also might want to make complex numbers out of fixed-points types, higher-precision real numbers, etc.

Answer 1

You can't properly implement many of the std::complex operations on integers. E.g.,

template <class T>
T abs(const complex<T> &z);

for a complex<long> cannot have T = long return value when complex numbers are represented as (real,imag) pairs, since it returns the value of sqrt(pow(z.real(), 2) + pow(z.imag(), 2)). Only a few of the operations would make sense.

Even worse, the polar named constructor cannot be made reliable without breaking the default constructor and vice versa. The standard would have to specify that "complex integers" are Gaussian integers for them to be of any use, and that one of the constructors is severely broken.

Finally, how would you like your "complex integer division" served, and would you like a "complex remainder" with that? :)

Summarizing, I think it would be more sensible to specify a separate gaussian_int<T> type with just a few operations than graft support for integral T onto std::complex.