import math

def layerxt(p, h, utop, ubot):
  # returns [dx, dt, irtr]
  
  if p >= utop: return [0.0, 0.0, 0]
  elif h==0: return [0.0, 0.0, -1]
  else:
  
    b = 1.0/(ubot*h) - 1.0/(utop*h)
    
    def eta(u): return math.sqrt(u**2-p**2)
    def x(u): return eta(u)/(u*b*p)
    def t(u): return (math.log((u+eta(u))/p))/b
    
    if utop == ubot: return [h*p/eta(utop), h*utop**2/eta(utop), 1 ]
    elif p>=ubot: return [x(utop), t(utop), 2]
    else: return [x(utop) - x(ubot), t(utop)-t(ubot), 1]