What do you mean brute force?

We can compute these things using iteration or polynomial approximations (sufficient for 64 bit).

There is a loop of is it close enough or not something like that. It is a brute force. Atan2 purely looks like that to me.

It’s not just guessing, there is theory to prove convergence and rates of converge.

Many algorithms require iteration.

I don't think these functions are programmed as it looks like they are in their Math form. Atan2 is something like a line-to rotating, if the given point is close to any pixel of line-to, returns how many times the line to is rotated. It is almost a motion but an algorithm. This is why I'm telling it is a brute force.

> Sin/cos must be borders of sqrt(x²+y²). It is also cached indeed

This doesn't make a ton of sense.

In what way do you think a sin function is computed? It is something that computed and cached in my opinion.

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

> 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.

It isnt good idea to store such values in code. I think it is something that computed when a programming environment is booting up. E.g. when you run "python", or install "python".

I try to understand how Math.sin works. There is Math.cos. It is sin +90 degrees. So not all of them is something that completes a big puzzle.

There's no nice way of saying this, and I mean no malice here, but I think you're exceptionally confused or ignorant, and I don't think it would be rewarding for either of us to continue this conversation.

It's ok if you don't reply If you don't have something to add to my saying. I think it is generated in like

for x in range(0, 90): for y in range(0, 90): if xx + yy < 90*90: # it is in circle

So for the each x, the one that has the greatest y will be the sin.

Something like floatrange(0,1,0.001) may work too.

> I think it is generated in like

You can think whatever you want, that's no substitute for being correct.

This is not about being correct. Posted article looks like a clickbait. I am digging what really is about. I would like to dig more Imho. I am looking for work here.

atan(x) = asin(x / sqrt(1+x*x))

So the asin is brute force. I think it is `atan` function. Written article explains nothing. Sqrt is also like that.

It looks like there is a reasonable explanation when it is written math form but there is no.