defmodule Piapprox do

  def iter_pi(epsilon) do
    pi = :math.pi
    leibniz_stream
      |> Stream.with_index
      |> Enum.reduce_while(0, fn
        ({i, _}, acc) when abs(pi - acc) >= epsilon ->
          {:cont, acc + i}
        ({_, n}, acc) ->
          {:halt, [n, Float.round(acc, 10)]}
      end)
  end

  defp leibniz_stream do
    Stream.unfold(1, fn
      n when rem(n,4) == 1 -> { 4/n, n+2 }
      n                    -> {-4/n, n+2 }
    end)
  end
end