Various Implementations of pow(x, y)

In this post, I discuss the implementation of function
double pow( double, int ).

Let's first consider the most simple case: y is a positive integer.
The naive and straightforward approach is working with a loop like following.

Next, we need consider all possible integers for y.

We can write a recursive function to calculate x raised to the power y.

The time complexities for all above 3 implementations are $O(n)$. Use of a temporary variable would help.

Now, the time complexity reduces to $O(\log n)$. How about non-recursive version? Yes, we can do it.

Actually, we can have one more implementation with bit operations!! Sounds amazing!