log

log.rb

class Real
  def log
    return if zero?
    _ = self
    return (- _).log if _ < zero
    if _ > 2 or _ < unity
      e = 0
      e, _ = e + 1, _ / 2 while _ > 2
      e, _ = e - 1, _ * 2 while _ < 1
      _.log + e * 2.log
    else
      _ = x = unity - inverse
      t = 1
      i, r = 1, 0
      until t.zero?
        r += t
        i += 1
        _ *= x
        t = _ / i
      end
      r
    end
  end
end