logistic_map

defmodule LogisticMap do
  @moduledoc """
  Documentation for LogisticMap.
  """

  @doc """
  calc logistic map.

  ## Examples

      iex> LogisticMap.calc(1, 61, 22)
      44

  """
  def calc(x, p, mu) do
    rem(mu * x * (x + 1), p) 
  end

  @doc """
  loop logistic map

  ## Examples

      iex> LogisticMap.loopCalc(10, 1, 61, 22)
      28

  """
  def loopCalc(num, x, p, mu) do
    if num <= 0 do
      x
    else
      loopCalc(num - 1, calc(x, p, mu), p, mu)
    end
  end

  @doc """
  Flow.map calc logictic map

  ## Examples

      iex> 1..3 |> LogisticMap.mapCalc(10, 61, 22, 1)
      [28, 25, 37]

  """
  def mapCalc(list, num, p, mu, stages) do
    list
    |> Flow.from_enumerable(stages: stages)
    |> Flow.map(& loopCalc(num, &1, p, mu))
    |> Enum.to_list
  end

  @doc """
  Flow.map calc logictic map

  ## Examples

      iex> 1..3 |> LogisticMap.mapCalc2(61, 22, 1)
      [28, 25, 37]

  """
  def mapCalc2(list, p, mu, stages) do
    list
    |> Flow.from_enumerable(stages: stages)
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Flow.map(& calc(&1, p, mu))
    |> Enum.to_list
  end

  @doc """
  Flow.map calc logictic map

  ## Examples

      iex> 1..3 |> LogisticMap.mapCalc3(61, 22, 1)
      [28, 25, 37]

  """
  def mapCalc3(list, p, mu, stages) do
    list
    |> Flow.from_enumerable(stages: stages)
    |> Flow.map(& (&1
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      |> calc(p, mu)
      ))
    |> Enum.to_list
  end


  @doc """
  Benchmark
  """
  def benchmark(stages) do
    IO.puts "stages: #{stages}"
    IO.puts (
      :timer.tc(fn -> mapCalc(1..0x2000000, 10, 6_700_417, 22, stages) end)
      |> elem(0)
      |> Kernel./(1000000)
    )
  end

  @doc """
  Benchmark
  """
  def benchmark2(stages) do
    IO.puts "stages: #{stages}"
    IO.puts (
      :timer.tc(fn -> LogisticMap.mapCalc2(1..0x2000000, 6_700_417, 22, stages) end)
      |> elem(0)
      |> Kernel./(1000000)
    )
  end


  @doc """
  Benchmark
  """
  def benchmark3(stages) do
    IO.puts "stages: #{stages}"
    IO.puts (
      :timer.tc(fn -> LogisticMap.mapCalc3(1..0x2000000, 6_700_417, 22, stages) end)
      |> elem(0)
      |> Kernel./(1000000)
    )
  end

  @doc """
  Benchmarks
  """
  def benchmarks() do
    [1, 2, 4, 8, 16, 32, 64, 128]
    |> Enum.map(& benchmark(&1))
    |> Enum.to_list
  end

  @doc """
  Benchmarks
  """
  def benchmarks2() do
    [1, 2, 4, 8, 16, 32, 64, 128]
    |> Enum.map(& benchmark2(&1))
    |> Enum.to_list
  end


  @doc """
  Benchmarks
  """
  def benchmarks3() do
    [1, 2, 4, 8, 16, 32, 64, 128]
    |> Enum.map(& benchmark3(&1))
    |> Enum.to_list
  end
end