October 31st, class 4

Fibonacci

defmodule Fibonacci do
  # def calc(0), do: 0
  # def calc(1), do: 1

  # def calc(n) when n > 1 do
  #   calc(n - 1) + calc(n - 2)
  # end

  def find(nth) do
    list = [1, 1]
    fib(list, nth)
  end

  defp fib(list, 2) do
    Enum.reverse(list)
  end

  defp fib(list, n) do
    [first_element, second_element | _rest] = list
    fib([first_element + second_element | list], n - 1)
  end

  def nth_v2(n) do
    find(n)
    |> Enum.reverse()
    |> hd()
  end
end

Fibonacci.find(2000)

Fibonacci.nth_v2(2000)

defmodule HeronMethod do
  def sqrt(n, error \\ 1.0e-10) do
    sqrt(n, error, 1.0, 0.5 * (1 + n))
  end

  defp sqrt(n, error, prev, new) when abs(new - prev) > error do
    sqrt(n, error, new, 0.5 * (new + n / new))
  end

  defp sqrt(_, _, _, new), do: new

  def pow(base, exponent) do
    base ** exponent
  end

  def cbcrt(x) do
    x ** (1 / 3)
  end
end

ExUnit.start(auto_run: false)

defmodule HeronMethodTest do
  use ExUnit.Case, async: false

  describe "Testing the square root function" do
    test "the square root of 9 is 3.0" do
      assert HeronMethod.sqrt(9) == 3.0
    end
  end

  describe "Testing the power function" do
    test "3 raised to the power of 2 is 9" do
      assert HeronMethod.pow(3, 2) == 9
    end
  end

  describe "Testing the cubic root function" do
    test "the cubic root of 27 is 3.0" do
      assert HeronMethod.cbcrt(27) == 3.0
    end

    test "the cubic root of 64 is 4.0" do
      assert_in_delta HeronMethod.cbcrt(64), 4.0, 0.1
    end
  end
end

ExUnit.run()

HeronMethod.sqrt(16)