DSP Robotics Support

I didn't know how to describe it in the subject line. I'm currently training filter design. I started with impulse response, did a function, then switched to audible. The result of what I did is that the input signal gets nice rich overtones, the more you drive the module. But what is it? How could it be named?
It obviously isn't a filter, since (a) it doesn't filter anything out, but adds to the original signal, and (b) it only works with sinusoidal input signals (because the function uses sinusoidal on the input, too. Ah, just see it for yourself. I'm bad at describing).

1) What is it?
2) Does it introduce aliasing? It shouldn't, but I'm insecure.
3) How would I go about generalizing, so that it behaves the same, no matter the input signal? Meaning, it should produce the same overtones even on saw, square, etc. I know why it mathematically can't work. So please don't tell me why it doesn't, but rather how it would.

1.
It is a simple distortion module. When you simplify the code you get:

recently I've seen fairly similar code used in modeling valve distortion.

2.
Yes, as all simple distortion algorithms like this, it introduces a hell of an aliasing.
3.
try multi band processing. Split incoming audio into multiple band using hpf/lpf and apply the distortion to those sections.

Personally I think that aliasing is not necessarily bad in distortion devices. It adds to the dirty sound. However, an effective measure to avoid aliasing from distortion is oversampling. There is not much else, really,