data_matrix

defmodule DataMatrix.ReedSolomon do
  import Bitwise

  alias DataMatrix.GaloisField

  @doc """
    iex> DataMatrix.ReedSolomon.encode(<<142, 164, 186>>, 5)
    <<114, 25, 5, 88, 102>>
  """
  def encode(data, length) do
    coefficients = gen_poly(length)

    Enum.reduce(
      :binary.bin_to_list(data),
      Stream.cycle([0]) |> Enum.take(length + 1),
      fn codeword, acc ->
        k = Enum.at(acc, 0) ^^^ codeword

        acc =
          for j <- 0..(length - 1),
              do: Enum.at(acc, j + 1) ^^^ prod(k, elem(coefficients, length - j - 1))

        Enum.concat(acc, [0])
      end
    )
    |> Enum.take(length)
    |> :binary.list_to_bin()
  end

  def gen_poly(nc) do
    # coefficients
    c = Tuple.duplicate(0, nc + 1)

    Enum.reduce(1..nc, put_elem(c, 0, 1), fn i, c ->
      c = put_elem(c, i, elem(c, i - 1))

      c =
        if i - 1 >= 1 do
          Enum.reduce((i - 1)..1, c, fn j, c ->
            value = elem(c, j - 1) ^^^ prod(elem(c, j), GaloisField.antilog(i))

            put_elem(c, j, value)
          end)
        else
          c
        end

      put_elem(c, 0, prod(elem(c, 0), GaloisField.antilog(i)))
    end)
  end

  defp prod(0, _) do
    0
  end

  defp prod(_, 0) do
    0
  end

  defp prod(a, b) do
    GaloisField.antilog(rem(GaloisField.log(a) + GaloisField.log(b), 255))
  end
end