Improved quadratic function solver; added wrapper for math.sqrt()

advtrains/helpers.lua

@@ -398,13 +398,22 @@ function advtrains.decode_pos(pts)
 	return vector.new(dec(strx), dec(stry), dec(strz))
 end
 
+-- Solve quadratic equations (i.e. a*x^2 + b*x + c = 0)
 function advtrains.solve_quadratic_equation(a, b, c)
 	if not (a and b and c) then return nil end
+	if a == 0 then return {-c/b, -c/b} end -- avoid division by zero
 	local delta = (b*b - 4*a*c)
-	if delta < 0 then return nil end
+	if delta < 0 then return {-b/2/a,-b/2/a} end -- ignore imaginary part
 	return {((-b+math.sqrt(delta))/2/a),((-b-math.sqrt(delta))/2/a)}
 end
 
+-- safe square root
+-- Negative return values indicate imaginary numbers.
+function advtrains.safesqrt(a)
+	if a >= 0 then return math.sqrt(a) end
+	return 0 - math.sqrt(-a)
+end
+
 --[[ Benchmarking code
 local tdt = {}
 local tlt = {}

advtrains/lzb.lua

@@ -94,7 +94,7 @@ LZB point itself, and not related to the emergency brake.
 ]]
 function advtrains.lzb_map_entry(train, lzb)
 	local ret = {[0]={},[1]={},[2]={},[3]={}}
-	if (not train) or (not lzb) then return ret end
+	if not (train and lzb) then return ret end
 	local ti = train.index
 	local v0 = train.velocity
 	local v1 = lzb.spd
@@ -168,7 +168,7 @@ function advtrains.lzb_get_limit_by_entry(train, lzb)
 		local s = train.index - lzbmap[ret.lever].i
 		local a = advtrains.get_acceleration(train, ret.lever)
 		local v0 = lzbmap[ret.lever].v
-		ret.velocity = math.sqrt(2*a*s - v0*v0)
+		ret.velocity = math.abs(advtrains.safesqrt(2*a*s - v0*v0))
 	end
 	if ret.velocity < train.velocity -1 then ret.lever = ret.lever - 1 end
 	return ret

advtrains/trainlogic.lua

@@ -434,7 +434,7 @@ function advtrains.train_step_b(id, train, dtime)
 	else s = (v1*v1 - v0*v0)/2/a
 	end
 	train.ctrl.lzb = nil
-	if lzblimit.velocity and lzblimit.velocity < train.velocity then
+	if lzblimit.velocity and lzblimit.lever < train.lever then
 		tmp_lever = lzblimit.lever
 		while (lzbmap[tmp_lever].t > dtime) do
 			tmp_lever = tmp_lever - 1
@@ -457,7 +457,7 @@ function advtrains.train_step_b(id, train, dtime)
 	a = (v1 - train.velocity)/dtime
 	--- 4b. Move train and update train properties ---
 	local pdist = train.path_dist[math.floor(train.index)] or 1
-	local distance = s / pdist
+	local distance = pdist == 0 and s or s / pdist
 	train.lever = tmp_lever
 	train.velocity = v1
 	train.acceleration = a