-- cframe module
do
	local cf = CFrame.new
	local angles = CFrame.Angles
	local fromaxisangle = CFrame.fromAxisAngle
	local v3 = Vector3.new
	local nc = cf()
	local nv = v3()
	local components = nc.components
	local tos = nc.toObjectSpace

	local pi = math.pi
	local acos = math.acos
	local atan = math.atan
	local sin = math.sin
	local sqrt = math.sqrt
	local max = math.max
	local min = math.min
	local deg90 = pi/2

	local forward = v3(0,0,-1) -- arb

	function cframe.toquaternion(c)
		local x,y,z,xx,yx,zx,xy,yy,zy,xz,yz,zz = components(c)
		local tr = xx+yy+zz
		if tr>2.99999 then
			return x,y,z,0,0,0,1
		elseif tr>-0.99999 then
			local m = 2*(tr+1)^0.5
			return x,y,z,(yz-zy)/m,(zx-xz)/m,(xy-yx)/m,m/4
		else
			local qx = xx+yx+zx+1
			local qy = xy+yy+zy+1
			local qz = xz+yz+zz+1
			local m = (qx*qx+qy*qy+qz*qz)^0.5
			return x,y,z,qx/m,qy/m,qz/m,0
		end
	end
	local toquaternion = cframe.toquaternion

	function cframe.power(c,t)
		local x,y,z,xx,yx,zx,xy,yy,zy,xz,yz,zz = components(c)
		local tr = xx+yy+zz
		if tr > 2.99999 then
			return cf(t*x,t*y,t*z)
		elseif tr > -0.99999 then
			local m = 2*(tr+1)^5
			local qw = m/4
			local th = acos(qw)
			local s = (1-qw*qw)^0.5
			local c = sin(th*t)/s
			return cf(t*x,t*y,t*z,c*(yz-zy)/m,c*(zx-xz)/m,c*(xy-yx)/m,c*qw+sin(th*(1-t))/s)
		else
			local qx = xx+yx+zx+1
			local qy = xy+yy+zy+1
			local qz = xz+yz+zz+1
			local c = sin(deg90*t)/(qx*qx+qy*qy+qz*qz)^0.5
			return cf(t*x,t*y,t*z,c*qx,c*qy,c*qz,sin(deg90*(1-t)))
		end
	end
	local power = cframe.power

	function cframe.interpolate(c0,c1,t)
		return c0*power(tos(c0,c1),t)
	end
	local interpolate = cframe.interpolate

	function cframe.interpolator(c0,c1)
		if c1 then
			local x0,y0,z0,qx0,qy0,qz0,qw0 = toquaternion(c0)
			local x1,y1,z1,qx1,qy1,qz1,qw1 = toquaternion(c1)
			local x,y,z = x1-x0,y1-y0,z1-z0
			local c = qx0*qx1+qy0*qy1+qz0*qz1+qw0*qw1
			if c < 0 then
				qx0,qy0,qz0,qw0=-qx0,-qy0,-qz0,-qw0
			end
			if c < 0.9999 then
				local s = (1-c*c)^0.5
				local th = acos(c)
				return function(t)
					local s0 = sin(th*(1-t))/s
					local s1 = sin(th*t)/s
					return cf(x0+t*x,y0+t*y,z0+t*z,s0*qx0+s1*qx1,s0*qy0+s1*qy1,s0*qz0+s1*qz1,s0*qw0+s1*qw1)
				end
			else
				return function(t)
					return cf(x0+t*x,y0+t*y,z0+t*z,qx1,qy1,qz1,qw1)
				end
			end
		else
			local x,y,z,qx,qy,qz,qw = cframe.toquaternion(c0)
			if qw < 0.9999 then
				local s = (1-qw*qw)^0.5
				local th = acos(qw)
				return function(t)
					local s1 = sin(th*t)/s
					return cf(t*x,t*y,t*z,s1*qx,s1*qy,s1*qz,sin(th*(1-t))/s+s1*qw)
				end
			else
				return function(t)
					return cf(t*x,t*y,t*z,qx,qy,qz,qw)
				end
			end
		end
	end
	local interpolator = cframe.interpolator

	function cframe.pitch(c)
		local v = c.lookVector
		return atan(v.Y/sqrt(v.X^2+v.Z^2))
	end
	local pitch = cframe.pitch

	function cframe.fromtool(t)
		local gp = t.GripPos
		local gr = t.GripRight
		local gu = t.GripUp
		local gf = t.GripForward
		local x,y,z = gp.x,gp.y,gp.z
		local xx,xy,xz = gr.x,gu.x,-gf.x
		local yx,yy,yz = gr.y,gu.y,-gf.y
		local zx,zy,zz = gr.z,gu.z,-gf.z
		return cf(x,y,z,xx,xy,xz,yx,yy,yz,zx,zy,zz)
	end
	local fromtool = cframe.fromtool

	function cframe.totool(c,t)
		local x,y,z,xx,xy,xz,yx,yy,yz,zx,zy,zz = components(c)
		local gp = v3(x,y,z)
		local gr = v3(xx,yx,zx)
		local gu = v3(xy,yy,zy)
		local gf = v3(-xz,-yz,-zz)
		if t then
			t.GripPos = gp
			t.GripRight = gr
			t.GripUp = gu
			t.GripForward = gf
		end
		return {gp,gr,gu,gf}
	end
	local totool = cframe.totool

	local function tableshift(t0,p)
		local t1 = {}
		for i=1,#t0 do
			table.insert(t1,i,t0[i+p > #t0 and (i+p)%#t0 or i+p])
		end
		return t1
	end

	function cframe.shift(c,p)
		local x0,y0,z0,xx0,xy0,xz0,yx0,yy0,yz0,zx0,zy0,zz0 = components(c)
		local v = tableshift({x0,y0,z0},p)
		local x = tableshift({xx0,yx0,zx0},p)
		local y = tableshift({xy0,yy0,zy0},p)
		local z = tableshift({xz0,yz0,zz0},p)
		local x1,y1,z1 = unpack(v)
		local xx1,xy1,xz1 = unpack(x)
		local yx1,yy1,yz1 = unpack(y)
		local zx1,zy1,zz1 = unpack(z)
		return cf(x1,y1,z1,xx1,xy1,xz1,yx1,yy1,yz1,zx1,zy1,zz1)
	end
	local shift = cframe.shift

	function cframe.solve(originCF,targetPos,l1,l2)
		local localized = originCF:pointToObjectSpace(targetPos)
		local localizedUnit = localized.unit
		local l3 = localized.magnitude
		local axis = forward:Cross(localizedUnit)
		local angle = acos(-localizedUnit.Z)
		local planeCF = originCF*fromaxisangle(axis, angle)
		if l3 < max(l2,l1)-min(l2,l1) then
			return planeCF*cf(0,0,max(l2,l1)-min(l2,l1)-l3),-pi/2,pi
		elseif l3 > l1+l2 then
			return planeCF*cf(0,0,l1+l2-l3),pi/2,0
		else
			local a1 = -acos((-(l2*l2)+(l1*l1)+(l3*l3))/(2*l1*l3))
			local a2 = acos(((l2 *l2)-(l1*l1)+(l3*l3))/(2*l2*l3))
			return planeCF,a1+pi/2,a2-a1
		end
	end
	local solve = cframe.solve

	local function isnan(x)
		return x ~= x
	end

	function cframe.checknan(c)
		local comp = {c:components()}
		local nan = false
		for c=1,#comp do
			local v = comp[c]
			if isnan(v) then
				print("value is nan")
				nan = true
			end
		end
		return nan
	end
	local checknan = cframe.checknan
end