std.complex

[John Colvin]

On Tuesday, 26 November 2013 at 11:22:38 UTC, Joseph Rushton 
Wakeling wrote:
> On 26/11/13 02:02, Andrei Alexandrescu wrote:
>> If you got the blessing of some complex number expert, that 
>> would be great.
>
> I'm in Italy, I could ask the pope ... :-)
>
> As far as I can see the behaviour of std.complex.Complex is 
> consistent both with C++'s std::complex and with D's own 
> internal cfloat/cdouble/creal types.  The only case we don't 
> cover with std.complex is that of multiplying a complex number 
> with a purely imaginary one (the equivalent of multiplying, 
> say, a creal and an ireal; multiplying a creal and a creal, 
> even if the real part of the latter is 0, will give the same 
> results as std.complex).
>
> We _could_ tweak Complex internally so that in the event that 
> its real part is 0, it behaves like a purely imaginary number, 
> and if its imaginary part is 0, it behaves like a purely real 
> number; but that's problematic for reasons already discussed, 
> because it doesn't distinguish between a purely imaginary 
> number versus one where the real part is so vanishingly small 
> that FP considers it to be 0.
>
> (It also leaves std.complex' behaviour incompatible with 
> std::complex and other library implementations, though I guess 
> that's less of a concern so long as we think what std.complex 
> does is right.)
>
> So, as other people have suggested, really the only thing we 
> can reasonably do is to define a separate Imaginary type -- or 
> get round the problems with the built-in complex and imaginary 
> types.  It is really a shame if they are as problematic as I've 
> heard. :-(

It seems to me that one really shouldn't special case for 
absolute values when dealing with floating point. A floating 
Imaginary type and an integer Complex type - both in std.complex 
- are the correct solutions IMO.