Current complex division leads to wrong results

[daingun]

Current complex number division implementation causes intermediate values to over/underflow leading to NaN.

use crate::num_complex::Complex;
use num_complex;
fn main() {
    let a = Complex::<f32>::new(489286830000000000000.0, 0.);
    let b = Complex::<f32>::new(73718980000000000000.0, 0.);
    println!("{}", a / b); // prints NaN+0i, should be around 6.6+0i
}

Please see this papers for a better implementation:
https://www.scilab.org/tutorials/scilab-not-naive-%E2%80%93-tutorial
https://arxiv.org/abs/1210.4539

Here a link to rust playground with a comparison of the two implementations: https://play.rust-lang.org/?version=stable&mode=debug&edition=2018&gist=1b4d0ea769f0704f0902718796effce4

[cuviper]

The problem is mostly that Div is generic for all T: Num, and Rust doesn't have specialization (yet) for us to do anything better for floating point types. This was discussed in #23, and as a result #41 added simple finv() and fdiv() methods for T: Float that do get much closer.

In this playground, the real-only division gets 6.6371894, as does your smith implementation, while fdiv gets 6.63719. I would be open to your improvements in fdiv if you'd like to open a pull request.

[daingun]

Thank you for the answer, I checked the old issues but i didn't found #23. At the moment I can switch to fdiv().
I'm closing this issue since it is a duplicate, if I implement the Smith's method I will open a pull request.