Joe Celko's Thinking in Sets: Auxiliary, Temporal, and Virtual Tables in SQL

5.6. Interpolation

In a previous section, I mentioned that books used to have lookup tables in the back for functions. But what happens when you have a value that is not in those tables? Before pocket calculators and personal computers became cheap and powerful, we used interpolation.

This technique is a way of guessing the results of a function that lies between two known values. Let’s call the two known functional values a and b, and their results from the function f(a) and f(b), and try to find f(x), where (a < = x < = b), but x is not in the table. We have to make a lot of assumptions about the function. It has to be continuous over the interval [a, b] and behave in a smooth fashion. Thank goodness, polynomials and most other common functions ...