sqrt() approximation

[nackstein]

Hello,
I'm not sure if it's a bug or a known rounding behavior.
If I compute the sqrt() of a complex number -9+0i the correct solution should be 0+3i
but with this module (I used num crate) I got:
0.00000000000000018369701987210297+3i

As far as I know some math lib implement hard-coded case for some exact value.
Did you considered doing the same?

Luigi

[cuviper]

That's rounding error -- we convert to polar to perform the operation and then convert back. So -9+0i = 9e^iπ, then the square root is 3e^iπ/2 = 0+3i. However, those irrational angles can't be precisely represented, so the conversions are slightly inaccurate.

But yes, I think we could add a special case when the input has zero imaginary value. The principal square root of a positive real is a positive real, and for a negative real it is a positive imaginary. Then we wouldn't have any loss beyond the scalar Float::sqrt itself.