# MIT License
#
# Copyright (c) 2018 Knoxen
#
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# of this software and associated documentation files (the "Software"), to deal
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# SOFTWARE.

defmodule Puid.Entropy do
  @moduledoc """
  [Entropy](https://en.wikipedia.org/wiki/Entropy_(information_theory)) related calculations

  The implementation is based on mathematical approximations to the solution of what is often
  referred to as the [Birthday
  Problem](https://en.wikipedia.org/wiki/Birthday_problem#Calculating_the_probability).

  """

  alias Puid.CharSet

  @doc """
  Entropy bits for generating a `total` number of instances with the given `risk` of repeat

  The total size of the instance pool is 2<sup>bits</sup>.

  ## Example

      iex> Puid.Entropy.bits(10.0e6, 1.0e12)
      85.37013046707142

  """
  @spec bits(pos_integer, pos_integer) :: float()
  def bits(1, _), do: 0

  def bits(_, 1), do: 0

  def bits(total, risk) when is_number(total) and is_number(risk) do
    n =
      cond do
        total < 1000 ->
          :math.log2(total) + :math.log2(total - 1)

        true ->
          2 * :math.log2(total)
      end

    n + :math.log2(risk) - 1
  end

  @doc """

  Entropy bits of a string of `len` generated from characters `charset`, where `charset` is
  either an pre-defined `Puid.CharSet` or a string of unique characters.

  The character set must be comprised of unique symbols, and it is assumed each symbol in the
  character set has equal probability of occurrence (which maximizes entropy).

  ## Example

      iex> Puid.Entropy.bits_for_length(14, :alphanum)
      {:ok, 83}

      iex> Puid.Entropy.bits_for_length(14, "dingosky")
      {:ok, 42}

  """
  @spec bits_for_length(non_neg_integer(), atom() | String.t()) ::
          {:ok, non_neg_integer()} | {:error, Puid.reason()}

  def bits_for_length(len, charset) when -1 < len and (is_atom(charset) or is_binary(charset)) do
    case bits_per_char(charset) do
      {:ok, ebpc} ->
        {:ok, (len * ebpc) |> trunc()}

      error ->
        error
    end
  end

  @doc """

  Same as `Puid.Entropy.bits_for_length/2` but either returns the integer __bits__ or raises a
  `Puid.Error`

  ## Example

      iex> Puid.Entropy.bits_for_length!(14, :alphanum)
      83

      iex> Puid.Entropy.bits_for_length!(14, "dingosky")
      42

  """
  @spec bits_for_length!(non_neg_integer(), atom() | String.t()) :: non_neg_integer()
  def bits_for_length!(len, charset) when -1 < len and (is_atom(charset) or is_binary(charset)) do
    case(bits_for_length(len, charset)) do
      {:ok, ebpc} ->
        ebpc

      {:error, reason} ->
        raise Puid.Error, reason
    end
  end

  @doc """

  Entropy bits per character where `charset` is either an pre-defined `Puid.CharSet` or a string of
  unique characters.

  The character set must be comprised of unique symbols, and it is assumed each symbol in the
  character set has equal probability of occurrence (which maximizes entropy).

  Returns `{:ok, bits}`; or `{:error, reason}` if `arg` is either an unrecognized pre-defined
  `Puid.CharSet` or a string of non-unique characters.

  ## Example

      iex> Puid.Entropy.bits_per_char(:alphanum)
      {:ok, 5.954196310386875}
     
      iex> Puid.Entropy.bits_per_char("dingosky")
      {:ok, 3.0}

  """
  @spec bits_per_char(atom() | String.t()) :: {:ok, float()} | {:error, Puid.reason()}
  def bits_per_char(charset)

  def bits_per_char(charset) when is_atom(charset) do
    case CharSet.chars(charset) do
      :undefined ->
        {:error, "Invalid: charset not recognized"}

      chars ->
        {:ok, ebpc(chars)}
    end
  end

  def bits_per_char(chars) when is_binary(chars) do
    if CharSet.unique?(chars),
      do: {:ok, ebpc(chars)},
      else: {:error, "Invalid: chars not unique"}
  end

  @doc """
  Same as `bits_per_char/1` but either returns the `bits` or raises a `Puid.Error`

  ## Example

       iex> Puid.Entropy.bits_per_char!(:alphanum)
       5.954196310386875
     
       Puid.Entropy.bits_per_char!("dingosky")
       3.0

  """
  @spec bits_per_char!(atom() | String.t()) :: float()
  def bits_per_char!(charset)

  def bits_per_char!(arg) do
    case bits_per_char(arg) do
      {:ok, ebpc} ->
        ebpc

      {:error, reason} ->
        raise Puid.Error, reason
    end
  end

  defp ebpc(chars) do
    chars |> String.length() |> :math.log2()
  end

  @doc """

  Length needed for a string generated from `charset` to have `bits` of entropy.

  The character set must be comprised of unique symbols, and it is assumed each symbol in the
  character set has equal probability of occurrence (which maximizes entropy).

  ## Example

      iex> Puid.Entropy.len_for_bits(128, :alphanum)
      {:ok, 22}

      iex> Puid.Entropy.len_for_bits(128, "dingosky")
      {:ok, 43}

  """
  @spec len_for_bits(non_neg_integer(), atom() | String.t()) ::
          {:ok, non_neg_integer()} | {:error, Puid.reason()}
  def len_for_bits(bits, charset) when -1 < bits and (is_atom(charset) or is_binary(charset)) do
    case bits_per_char(charset) do
      {:ok, ebpc} ->
        {:ok, (bits / ebpc) |> :math.ceil() |> round()}

      error ->
        error
    end
  end

  @doc """

  Same as `Puid.Entropy.len_for_bits/2` but either returns the integer __len__ or raises a
  `Puid.Error`

  ## Example

      iex> Puid.Entropy.len_for_bits!(128, :alphanum)
      22

      iex> Puid.Entropy.len_for_bits!(128, "dingosky")
      43

  """
  @spec len_for_bits!(non_neg_integer(), atom() | String.t()) :: non_neg_integer()
  def len_for_bits!(bits, charset) when -1 < bits and (is_atom(charset) or is_binary(charset)) do
    case len_for_bits(bits, charset) do
      {:ok, len} ->
        len

      {:error, reason} ->
        raise Puid.Error, reason
    end
  end
end