defmodule Fluxion.Math do
  @moduledoc """
  This module defines some floating-point operations used in this package and
  its supporting tests.
  """

  @epsilon 1.0e-15

  @doc """
  Compare two floating point numbers for equality, allowing for small
  deviations.

  ## Examples

      iex> Fluxion.Math.is_equal(0, 0)
      :true

      iex> Fluxion.Math.is_equal(1, 2)
      :false

      iex> Fluxion.Math.is_equal(1, 2, 1)
      :true

      iex> Fluxion.Math.is_equal(0.3, 0.1 + 0.2)
      :true

      iex> Fluxion.Math.is_equal(10, 10 + 1.0e-6)
      :false
  """
  @spec is_equal(number, number, number) :: true | false
  def is_equal(a, b, epsilon \\ @epsilon) do
    diff = abs(a - b)

    cond do
      a === 0 || b === 0 ->
        diff < epsilon

      true ->
        diff / max(max(a, b), epsilon) < epsilon
    end
  end
end