function fact(z)
	z=z+1
    local m=math
	local pi,e,f=m.pi,m.exp(1),m.floor
	local g = 7
	local p = {0.99999999999980993, 676.5203681218851, -1259.1392167224028,
     771.32342877765313, -176.61502916214059, 12.507343278686905,
     -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7}
    if z<0.5 then
		if z<0 and f(z)==z then return m.huge end
        return pi/(m.sin(pi*z)*fact(-z))
    else
        z=z-1
        x=p[1]
        for i=1,g+1 do
            x=x+p[i+1]/(z+i)
		end
		t=z+g+0.5;r=m.sqrt(2*pi)*m.pow(t,z+0.5)*m.exp(-t)*x
        return (f(z)==z) and f(r) or r
	end
end