.. _hw8:

Homework 8 - A Recursive Function
===================================================================

.. seealso:: :ref:`recursion`

For this assignment, we will write our own function similar to the math
library function ``pow(a, k)``, which computes :math:`a^k`
where :math:`a` and :math:`k` are both scalar values. For our function,
we will restrict the scalar :math:`k` to the set of positive integer numbers.
The function prototype statement for our function might be::

    double my_pow(double, unsigned int);

The basis for our recursive algorithm is the simple mathematical relationship

.. math:: a^k = a^{{\left(k/2\right)}^2}.

By splitting :math:`k` in half each time :math:`k` is an even number,
the number of multiplications is greatly reduced.
Thus, our function should evaluate :math:`k` to one of the following cases.

**k == 0:** :math:`a^0 = 1`

**k == 1:** :math:`a^1 = a`

**k is an even number:** :math:`a^k = a^{{\left(k/2\right)}^2}`

**k is an odd number:** :math:`a^k = a\,a^{\left(k - 1\right)}`