std.complex

[Joseph Rushton Wakeling]

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. :-(