On Wednesday, 1 January 2014 at 23:32:58 UTC, Lars T. Kyllingstad
wrote:
I'm not 100% convinced that a pure imaginary type is the way to
go. You may be interested in reading a previous discussion,
where the subject of pure imaginary number support is brought
up:
http://forum.dlang.org/thread/flsf9u$jf$1...@digitalmars.com
I have read through that thread already, but thank you for
bringing it up -- it raises some issues that deserve an answer.
My own thoughts on the matter go something like this:
* There are calculations involving "pair of reals"
implementations of complex
numbers that generate spuriously incorrect results. They're
corner cases,
but they exist.
* A purely imaginary type allows those calculations to be
performed
correctly. It also allows more precise calculations in
general for cases
where the real part of a complex number is known to be 0.
* The idea of allowing imaginary literals but promoting them
to complex when
written to a variable sounds attractive but we can't
discount the
possibility that people will want to pass imaginary literals
to functions
or otherwise store them in variables, and later use them; if
they are
promoted to complex, calculations done with them may have
lesser precision
or even generate the aforementioned spurious results. I
don't think simply
writing to a variable should cause loss of precision like
this.
* You can do calculations involving purely real-valued numbers
and complex
numbers and not run into the same issues, because purely
real values are
supported. So you should be able to do the same with purely
imaginary
numbers.
* The lack of closure under various operations is annoying but
not
insurmountable.
I should add that as far as I'm concerned what I want is simply
to find the best possible way to represent and use purely
imaginary numbers in D. I don't mind if, having done that, the
code winds up being rejected, as long as the exercise proves
useful.
Of course, an alternative would be to tweak the internals of
Complex so that it can represent "purely real" and "purely
imaginary" types precisely.
I'm writing from a phone now so it's not really convenient to
explain at length, but I'll try to expand on the above in the
next days.
