defmodule Luhn do
  require Integer

  @spec valid?(integer, 2..36) :: boolean
  def valid?(number, base \\ 10) do
    checksum(number, base)
    |> Kernel.== 0
  end

  def checksum(number, base \\ 10)

  @spec checksum(integer, 2..36) :: integer
  def checksum(number, base) when is_integer(number) do
    number
    |> Integer.to_string(base)
    |> checksum(base)
  end

  @spec checksum(String.t, 2..36) :: integer
  def checksum(number, base) do
    number
    |> String.split("", trim: true)
    |> Enum.reduce([], fn(n, acc) -> [String.to_integer(n, base)|acc] end)
    |> double(base, 0)
    |> rem base
  end

  def double([], _, acc), do: acc
  def double([x], _, acc), do: x + acc
  def double([x,y|tail], base, acc), do: double(tail, base, acc + x + sum(y * 2, base))

  defp sum(number, base) when number >= base, do: number - base + 1
  defp sum(number, _), do: number
end