modulo.ex

defmodule Modulo do

  defmacro guard_safe_int_max(a, b) do
    quote do 
      div(unquote(a)+unquote(b) + abs(unquote(a) - unquote(b)), 2)
    end
  end

  defmacro int_sign(x) do
    quote do
      div(unquote(x), guard_safe_int_max(abs(unquote(x)), 1))
    end
  end

  defmacro floor_div(a, n) do
    quote do
      div(unquote(a), unquote(n)) + div(int_sign(rem(unquote(a), unquote(n)) * unquote(n)) - 1, 2)
    end
  end

  defmacro mod(a, n) do
    quote do
      unquote(a) - (unquote(n) * floor_div(unquote(a), unquote(n)))
    end
  end
end