[RESOLVED] Solve a cubic polynomial

[Kallog]

Sounds easy, but I can't quite do it reliably on the computer.

I'm using what I think is the Cardini algorithm. It first converts to the depressed form, then chooses one of 3 options depending on if some expression is <0, =0 or >0.

Problem is it's hard to do floating point comparisons safely, so some of my equations are ending up with the wrong number of solutions.

Is there a robust way to do it?

Oh, also I only need real solutions. Complex solutions should become 0. This also worries me a bit. I have a feeling rounding errors might cause a solution to have a very tiny imaginary component, then when I set it to zero I lose the entire real component.