On Monday, 16 April 2012 at 11:27:29 UTC, Stewart Gordon wrote:
On 16/04/2012 07:06, Lars T. Kyllingstad wrote:
<snip>
For any standard type (built-in or library) to be useful, it
has to actually be used for
something.
You mean someone has to use it in order to prove that it's
usable and therefore useful? Well, if a feature isn't usable,
it's probably due to something wrong with its design. And in
many cases it's a reason to rethink the design, rather than
throw the feature out of the window.
And in all my years of using D, I have never seen a *single*
real-world use of
the pure imaginary types.
How many of those years you spent "using" D did you spend
looking at other people's real-world applications written in it?
Of these, how many have a focus on number crunching?
And of these, how many use complex numbers?
This is why I said: "[...] if anyone can demonstrate that the
pure imaginary types are in fact used in a substantial body of
real-world code, I will be happy to change my stance [...]"
It's bound to be a rarely used feature. But "nobody's using
it" is a prime example of a self-fulfilling prophecy if it
leads to the feature's removal.
I'm not saying it is *never* useful. I'm saying I don't think
it's useful *enough* to warrant inclusion in the standard library.
Do you feel the SETI Institute should have given up years ago?
I don't really see the similarity between SETI and Phobos.
The reason the imaginaries are so seldomly used is precisely
because there are so few
things you can do with them. Basically, if you do anything
beyond addition and
subtraction, and multiplication with a real number, you are
back in the complex plane. And
if those operations are all you need, the real line is just as
good as the imaginary line,
and you might as well fake it with a real floating-point type.
This doesn't cover the case of multiplying a complex number by
an imaginary number. In the absence of imaginary types, one
would have to use complex(-z.im * k, z.re * k), just because z
* complex(0, k) isn't guaranteed to produce the correct result.
Seems a bit silly. Or have you another suggestion for dealing
with this?
Yes: Define Complex!T so it produces the desired result in each
case.
<snip>
It is true that the real line can be extended with elements
called plus and minus infinity
(affinely extended real line, see
https://en.wikipedia.org/wiki/Extended_real_number), and
the IEEE floats can be said to approximate this system, but
this does not generalise
directly to complex numbers. The extended complex plane (see
https://en.wikipedia.org/wiki/Riemann_sphere) only has one
"infinity".
<snip>
But the Riemann sphere is only one of the various possible
extended complex planes. You could just as well use the polar
circle of infinities, the cartesian square of infinities, or
the real projective plane model (by which -∞ = ∞, but ∞i,
∞(2+i), etc. are distinct).
My point exactly.
-Lars
