Don Clugston wrote:
On 25 March 2010 22:54, Andrei Alexandrescu <[email protected]> wrote:
Good call! Walter mentioned he should transfer some knowledge to Don in the
matter. Walter, please let us know how we can plan this.
Don suggested that the polar representation is very seldom used so we may as
well throw it away.
That's not the direct reason. The issue is that it's difficult to do
polar representation in a way which preserves numerically desirable
properties. For instance, the invariant if (x==x) assert( x == -
(-x)); MUST be preserved, but isn't true for a naive polar
representation. This rules out the use of floating point for the arg
-- you probably want to use some form of fixed point. Then you have
the problem that PI isn't exactly representable as a floating-point
number. And it's downhill from there.
Good points. When you think about it, most no-ops will end up being ops
for polar-form complex FP numbers if done naïvely.
-(-z)
z + 0
z.toCartesian.toPolar
And this is the reason why polar representation is seldom used -- it's
virtually always a bad idea.
Generally speaking the best way of doing polar representation is to
put a wrapper over a cartesian complex type!
I agree. I think having arg() and mod() as @properties of a Cartesian
complex type is good enough. They could even be setter properties, as
long as the documentation mentions the computational cost and numerical
error.
-Lars
On 03/25/2010 04:03 PM, Lars Tandle Kyllingstad wrote:
Is anyone working, or planning to do work, on std.complex? If not, and
if it is desirable, I could take a look at it. I guess the main thing
that is needed is to add overloaded operators. Is there anything else?
Also, I wonder: How do you feel about renaming "modulus" and "angle" to
"mod" and "arg"? I seldom hear or use the term "angle" in relation to
complex numbers. "Argument" and "phase" are much more common, and the
standard mathematical notation for the argument of a complex number is
Arg(z). Also, "mod" and "arg" are nice and short, like "re" and "im".
-Lars
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