defmodule Statistics.Math do

  @e 2.718281828459045
  @pi :math.pi

  @doc """
  Get square root

  return sqrt from Erlang

  ## Examples

      iex> Statistics.Math.sqrt(9)
      3.0
      iex> Statistics.Math.sqrt(99)
      9.9498743710662

  """
  defdelegate sqrt(num), to: :math

  @doc """
  Get power from Erlang

  This is needed because Elixir doesn't
  currently have the `**` operator

  ## Examples

      iex> Statistics.Math.pow(2,3)
      8.0
      iex> Statistics.Math.pow(9,9)
      387420489.0
      iex> Statistics.Math.pow(2,0)
      1
      iex> Statistics.Math.pow(-2, 1.5)
      -2.8284271247461903
      iex> Statistics.Math.pow(0, 5)
      0

  """
  def pow(_, 0), do: 1

  def pow(0, pow) when pow >= 0, do: 0

  # Erlang doesn't like raising negative numbers to non-integer powers
  def pow(num, pow) when num < 0 and is_float(pow) do
   :math.pow(-num, pow) * -1
  end

  defdelegate pow(num, pow), to: :math

  @doc """
  The constant *e*

  ## Examples

      iex> Statistics.Math.e
      2.718281828459045

  """
  def e do
    @e
  end

  @doc """
  The constant *pi*

  (returned from Erlang Math module)

  ## Examples

      iex> Statistics.Math.pi
      3.141592653589793

  """
  def pi do
    @pi
  end

  @doc """
  The natural log

  ( from Erlang Math module)

  ## Examples

      iex> Statistics.Math.ln(20)
      2.995732273553991
      iex> Statistics.Math.ln(200)
      5.298317366548036

  """
  defdelegate ln(i), to: :math, as: :log

  @doc """
  Exponent function

  Raise *e* to given power

  ## Examples

      iex> Statistics.Math.exp(5.6)
      270.42640742615254

  """
  defdelegate exp(x), to: :math

  @doc """
  Get a random number from erlang
  """
  defdelegate rand(), to: :random, as: :uniform

  @doc """
  Round a decimal to a specific precision

  ## Examples

      iex> Statistics.Math.round(0.123456, 4)
      0.1235

  """
  def round(x, precision) do
    p = pow(10, precision)
    :erlang.round(x * p) / p
  end

  @doc """
  Floor function

  ## Examples

      iex> Statistics.Math.floor(3.999)
      3.0

  """
  def floor(x) do
    f = :erlang.trunc(x) * 1.0
    cond do
      x - f >= 0 ->
        f
      x - f < 0 ->
        f - 1
    end
  end  

  @doc """
  Ceiling function

  ## Examples

      iex> Statistics.Math.ceil(3.999)
      4.0

  """
  def ceil(x) do
    f = :erlang.trunc(x) * 1.0
    cond do
      x - f > 0 ->
        f + 1
      x - f <= 0 ->
        f
    end
  end

  @doc """
  Get the absolute value of a number

  ## Examples

      iex> Statistics.Math.abs(-4)
      4

  """
  defdelegate abs(x), to: :erlang

  @doc """
  Factorial!
  """
  def factorial(n) when n == 0 or n == 1 do
    1
  end
  def factorial(n) do
    l = for i <- to_int(n)-1..1, do: i
    List.foldl(l, n, fn(x, acc) -> x*acc end)
  end

  @doc """
  Get the base integer from a float

  ## Examples

      iex> Statistics.Math.to_int(66.6666)
      66

  """
  defdelegate to_int(f), to: :erlang, as: :trunc

end