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numbers

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Numbers dispatches on any numeric type that follows the `Numeric` behaviour. This allows you to create composite types working with _any_ numeric type (Decimal, Ratio, Tensor, ComplexNum, ???)!

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numbers lib numbers helper.ex
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lib/numbers/helper.ex 

defmodule Numbers.Helper do

  @moduledoc """

  Helper functions that might make the implementation

  of Numbers for your own numberlike types easier.

  """



  @doc """

  Performs 'Exponentiation by Squaring',

  which is a reasonably fast algorithm to compute integer powers,

  by performing log(n) multiplication steps.



  Depends on an implementation existing of `Numbers.Protocols.Multiplication`,

  as well as (to support negative powers) an implementation of `Numbers.Protocols.Division`.

  """

  def pow_by_sq(num, integer_power)

  # Small powers

  def pow_by_sq(x, 1), do: x

  def pow_by_sq(x, 2), do: Numbers.Protocols.Multiplication.mult(x, x)

  def pow_by_sq(x, 3), do: Numbers.Protocols.Multiplication.mult(Numbers.Protocols.Multiplication.mult(x, x), x)

  def pow_by_sq(x, n) when is_integer(n), do: do_pow_by_sq(x, n)



  # Exponentiation By Squaring.

  defp do_pow_by_sq(x, n, y \\ 1)

  defp do_pow_by_sq(_x, 0, y), do: y

  defp do_pow_by_sq(x, 1, y), do: Numbers.Protocols.Multiplication.mult(x, y)

  defp do_pow_by_sq(x, n, y) when n < 0, do: do_pow_by_sq(Numbers.Protocols.Division.div(Numbers.Protocols.Multiplication.mult_id(x), x), Kernel.-(n), y)

  defp do_pow_by_sq(x, n, y) when rem(n, 2) == 0, do: do_pow_by_sq(Numbers.Protocols.Multiplication.mult(x, x), Kernel.div(n, 2), y)

  defp do_pow_by_sq(x, n, y), do: do_pow_by_sq(Numbers.Protocols.Multiplication.mult(x, x), Kernel.div((n - 1), 2), Numbers.mult(x, y))

end