Epsilon = 10e-16
ln10 = 2.30258509299404568401
def ln_h(x):
  '''
  ln函数泰勒换元展开
  :param x: 0<x
  :return:ln(x)
  '''
  def ln_h1(x):
    s2 = 0.0
    delta = x = (x - 1.0) / (x + 1.0)
    i = 0
    while fab_h(delta * 2) / (i * 2 + 1) > Epsilon:
      s2 += delta / (i * 2 + 1)
      delta *= x * x
      i += 1
    print(i)
    return 2 * s2
  coef = 0
  if x > 10:
    while x / 10 > 1:
      coef += 1
      x /= 10
    return ln_h1(x) + coef*ln10
  elif x < 1:
    while x * 10 < 10:
      coef += 1
      x *= 10
    return ln_h1(x) - coef*ln10
  else:
    return ln_h1(x)