We'll look at two performance tweaks for the Power1 class shown previously.

First, we need to switch to a better algorithm. Then, we will require a better algorithm combined with memoization, which involves a cache; therefore, the function becomes stateful. This is where callable objects shine.

The first modification is to use a divide-and-conquer design strategy. The previous version chopped the computation of steps.

For example, pow1(2,1024), the Power1 callable, performs 1,024 individual multiplication operations. We can optimize this down to 10 multiplications, a significant speedup.

Rather than simply multiplying by a fixed value, we'll use the fast exponentiation algorithm...