Linear interpolation

As I intend to use lookup tables for the DCO frequency and amplitude, I started looking for ways to do linear interpolation of the values in such a table to keep the number of entries low.

I may have mentioned it in a previous post, but I bought an early 80s digital sound creation book, and it has a thorough description of how to do this fast and efficiently. It is particulary space saving for symmetric waves such as sines but may be of some help even to me. Here is the text (for me to remember):