Complex.zero returns unexpeceted #sign

[jkthorne]

Bug Report

Some Complex numbers that have zeros return 0 and 0i but on the default zero case it returns NaN and NaNi. This was unexpected to me. After bringing it up on Discord it seems like it might be a bug.

Here is an example of an expected 0 sign. https://play.crystal-lang.org/#/r/cjvt

require "complex"

p Complex.new(1, 0).sign

output:

(1.0 + 0.0i)

Here is the case I am not sure if it is correct. https://play.crystal-lang.org/#/r/cjvv

require "complex"

p Complex.zero.sign

output

(-NaN - -NaNi)

[martinhart]

Forgive me if I'm not fully understanding the problem, but what would we expect the correct output to be here? #sign is currently implemented using division, and division by 0 is resulting in NaN in this case.

[asterite]

I think (0, 0) is expected to be returned.

That said, sign for Complex is a bit strange, I think we should remove that method.

[beta-ziliani]

According to the wikipedia

For reasons of symmetry, and to keep this a proper generalization of the signum function on the reals, also in the complex domain one usually defines, for z = 0:
sgn ⁡ ( 0 + 0 i ) = 0

So I would classify this as an outright bug. @wontruefree out of curiosity, what brought you to this function?

[jkthorne]

@beta-ziliani I have been looking for undocumented and under documented features and trying to understand them and add docs for them

[beta-ziliani]

My physicist wife tells me this function is useful to have, so it's better to fix it and document it.