How to have nice dead-zoning for joystick input

deadzoner.js

// Nice deadzoning
//	raw contains the x and y of the joystick
//	dead is the threshold (0.2 for good results)
function deadZoner(raw, dead) {
	// d2 is the square of the magnitude of raw
	var d2 = raw.x*raw.x + raw.y*raw.y;
	
	// If d2 is lower than the deadzone squared, then we're inside the deadzone
	// (Also check against zero, in case we're given a zero deadzone)
	if (d2<dead*dead || d2<0){
		// We're inside the deadzone, return zero
		return {x: 0, y:0};

	} else {
		// We're out of the deadzone, let's smooth out that janky threshold
		
		// d2 is squarerooted to get actual distance from zero
		var d = Math.sqrt(d2);

		// Normalise raw input
		var nx = raw.x/d;
		var ny = raw.y/d;

		// Rescaled so (dead->1) becomes (0->1)
		d = (d-dead)/(1-dead);
		
		// and clamped down so we get 0 <= d <= 1
		d = Math.min(d,1);
		
		// Apply a curve for a smoother feel (as suggested by (Gibgezr)[https://github.com/Gibgezr]
		// Uncomment the following line and see if your game feels better
		// d = d*d

		// Scale normalised input and return
		return {
			x: nx*d,
			y: ny*d
		}
	}
}

deadzoner.lua

-- Nice deadzoning
--	raw contains the x and y of the joystick
--	dead is the threshold (0.2 for good results)
function deadZoner(raw, dead)
	-- d2 is the square of the magnitude of raw
	local d2 = raw.x*raw.x + raw.y*raw.y
	
	-- If d2 is lower than the deadzone squared, then we're inside the deadzone
	-- (Also check against zero, in case we're given a zero deadzone)
	if d2<dead*dead or d2<0 then
		-- We're inside the deadzone, return zero
		return {x = 0, y = 0}

	else
		-- We're out of the deadzone, let's smooth out that janky threshold
		
		-- d2 is squarerooted to get actual distance from zero
		local d = math.sqrt(d2)

		-- Normalise raw input
		local nx = raw.x/d
		local ny = raw.y/d

		-- Rescaled so (dead->1) becomes (0->1)
		d = (d-dead)/(1-dead)
		
		-- and clamped down so we get 0 <= d <= 1
		d = math.min(d,1)
		
		-- Apply a curve for a smoother feel (as suggested by (Gibgezr)[https://github.com/Gibgezr]
		-- Uncomment the following line and see if your game feels better
		-- d = d*d

		-- Scale normalised input and return
		return {
			x = nx*d,
			y = ny*d
		}
	end
end

Since this is aimed at beginning game programmers, I’ll mention this: this is great if all you need is a linear response, but for things like player and camera movement/rotation, a pronounced response curve is normally used, so we’d do something like squaring the deadzoned x,y pair before using it. Offhand I can’t think of anytime I’d require a linear response, even adjusting UI sliders is easier with a curved response, so if folks try dropping this into their projects and find it feels clunky, try squaring those values AFTER deadzoning.

Thanks (Gibgezr)[https://github.com/Gibgezr] for the suggestion!
It's not entirely part of the problem that deadzoning tries to fix, but it's useful and does tend to make thing feel better
I added it commented, and users are encouraged to uncomment the line to see if their controls feels better