> In what way do you think a sin function is computed?

In some way vaguely like this: https://github.com/jeremybarnes/cephes/blob/master/cmath/sin...

> I think it is stored like sintable[deg]. The degree is index.

I can think of a few reasons why this is a bad idea.

1. Why would you use degrees? Pretty much everybody uses and wants radians.

2. What are you going to do about fractional degrees? Some sort of interpretation, right?

3. There's only so much cache available, are you willing to spend multiple kilobytes of it every time you want to calculate a sine? If you're imagining doing this in hardware, there are only so many transistors available, are you willing to spend that many thousands of them?

4. If you're keeping a sine table, why not keep one half the size, and then add a cosine table of equal size. That way you can use double and sum angle formulae to get the original range back and pick up cosine along the way. Reflection formulae let you cut it down even further.

There's a certain train of thought that leads from (2).

a. I'm going to be interpreting values anyway

b. How few support points can I get away with?

c. Are there better choices than evenly spaced points?

d. Wait, do I want to limit myself to polynomials?

Following it you get answers "b: just a handful" and "c: oh yeah!" and "d: you can if you want but you don't have to". Then if you do a bunch of thinking you end up with something very much like what everybody else in these two threads have been talking about.