Bug 3690 – Folding Complex!(Complex!T) to Complex!T

This is a suggestion for a minor change to std.complex that can be implemented with the current DMD, by simply copy-pasting the small code snippet at the bottom. The idea is to make Complex!(Complex!T) evaluate to just Complex!T. The rationale is: 1. Complex!(Complex!T) doesn't make sense at all. 2. Just like the real line is a subspace of the complex plane, the complex plane is also, strictly speaking, a subspace of itself. 3. It would make it possible to write functions like: Complex!T sqrt(T)(T x) { ... } auto i = sqrt(-1); auto z = sqrt(i); For such a simple example it is of course better to write ordinary function overloads, but more complicated cases quickly cause trouble for DMD's IFTI. The real-life case that inspired me to write this request is the eigenvalues() function in SciD that calculates the eigenvalues of a matrix. It would make life simpler for me (and for the compiler) if I could write it like Complex!T[] eigenvalues(T)(Matrix!T m, Complex!T[] buffer=null) { ... } and test for the complex-ness of T using static ifs inside the function body, thus reducing the need for complicated IFTI with multiple function declarations. (The problem here is when the user does not give the optional parameter.) Here's the code to implement the feature: // Fold Complex!(Complex!T) to Complex!T template Complex(Num : Complex!(U, Representation.cartesian), Representation rep=Representation.cartesian, U) { alias Complex!(U, rep) Complex; } template Complex(Num : Complex!(U, Representation.polar), Representation rep=Representation.cartesian, U) { alias Complex!(U, rep) Complex; }

A complex number of complex number is a quaternion. (http://en.wikipedia.org/wiki/Quaternion#Quaternions_as_pairs_of_complex_numbers).

Implemented in the new std.complex, included since DMD 2.044.