overdrive~ with near-zero or negative values

Hello there!
Can someone explain to me what exactly happens when the overdrive~ object is used with near-zero or negative values?
I tested this with a simple sine wave and a scope to see what actually happens and read the description, but some part
of what it does still seems to elude me. If positive values amplify and limit/clip the signal between -1/1 values, what does a negative value do
to the signal and why does it get so very loud so very fast?
I'm mostly interested in this because the audible results are very interesting, harmonically rich but distorted sounds
and i'd like to understand what is happening waveshaping-wise and how harshly it affects the waveform/pitch of the input sound.