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Simple deadzone applied to each axis separately. The deadzone is essentially a box. The value of each axis is re-scaled so it's 0 at the deadzone and 1 at the end of travel.
I think ideally the deadzone should be a circle. I tried that but I realized my controller would be maxed out on one axis and still output a non-zero value on another, so I couldn't use trig to compute the proper deadzone values for each axis. And this will likely change from controller to controller, so I think for this to work properly it'd be necessary to have something similar to Dolphin's deadzone thingamajig.