powc of zero returns nan

[domna]

When I execute the following line

Complex64::from(0.).powc(Complex64::from(1.))

I get nan as the output.

Shouldn't this be zero instead of nan?

[cuviper]

Ouch, that's a big oversight. This probably comes from the implementation's r.ln() when r (the magnitude) is zero. We should probably add a special case for this... I'm not sure about how to handle the minutia of float +/-0 though. Maybe there's precedent we can draw from libraries in other languages.

[domna]

Yes I was also suspecting the ln as well. It seems that C does just a check for zero and uses a similar formula: https://github.com/eblot/newlib/blob/2a63fa0fd26ffb6603f69d9e369e944fe449c246/newlib/libm/complex/cpowf.c#L47

I'm currently using a workaround for this:

trait ComplexPower {
    fn pc(self, exp: Complex64) -> Complex64;
}

impl ComplexPower for Complex64 {
    fn pc(self, exp: Complex64) -> Complex64 {
        if self.re == 0. && self.im == 0. {
            return Complex64::from(0.);
        }
        self.powc(exp)
    }
}

which does exactly this and it seems to be fine for me (but should rather use the abs of the complex number, though). If I'm thinking correctly, I think for floats which are very small but not exactly zero it is fine as the ln will be still be properly defined but negative and very large (which we want here). Negative residuals will not occur as it uses the amplitude in the implementation. I could prepare a PR for this.