🚀 go-pugleaf

Peter Froelich wrote:
[snip]
>   All books on (practical) numerical mathematics that I've come across do
>   fine with REAL.
>
>AFAIK  (please correct me) not even the various *-XDS languages by Kuchling
>et.al.   have  a  COMPLEX type, even it they were specifically tailored for
>numerics (exact rounding in an interval arithmethic).
>
>   Although  a  complex  type seems pleasing, I'm not yet convinced that it
>really  would  cause  a lot of algorithms to be converted to actually using
>COMPLEX  instead  of  REAL.   Please  give  me  an  example  algorithm that
>*seriously* benefits from a COMPLEX type.
[snip]
>                  _
>By(T)e...   /| _ //3000 /\ People who use Pascal for serious programming |\
>   Peter... \| \X/\miga \/ fall into a fatal trap.  (Brian W. Kernighan) |/

Well, I am working mainly in integrated optics and quantum electronics.
Nearly all the equations in this field use complex numbers.
You can do it using reals, but this complicates things a lot.
Being able to express my equations and algorithms directly using a
complex type would simplify my program writing a lot.

And your argument about people not using complex in numerical analysis
books is irrelevant. These books are concerned with maximum speed 
and efficiency. I will trade a 30 % slowdown on execution for a 100 %
speedup on writing my programs (especially since my execution times
are typically a few seconds up to a a minute).

Thus, while it may be true that a complex type is not always the best solution,
there are a lot of situations when the gain in legibility and writing
speed of the program more than justifies the slight loss of execution
speed. This is exactly the same trade-off as when one uses a high-level
language versus assembly code.

Jean-Pierre
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