musl VS vectrig

well OK, but figure this one out:

https://github.com/ifduyue/musl/blob/master/src/ctype/casema...

How do you regenerate it when the Unicode version changes?

musl-libc

https://git.musl-libc.org/cgit/musl (musl, another open source implementation, I've heard this one has more readable code)

Thanks for explaining this. I actually wrote a SIMD implementation of trig functions years ago, using the techniques you describe.

You can check it out: https://github.com/jeremysalwen/vectrig

I compared several different methods of generating polynomials of different sizes for speed and precision (spoilers: taylor series were the worst and minimax polynomials (Remez algorithm) were the best).

Another (surprising) thing which I learned during the project was that the range reduction was just as (if not more) important to the accuracy of the implementation than the polynomial. If you think about it, you will realize that it's actually pretty difficult to quickly and accurately compute the sin of large numbers like 2^50.

I also tried to directly optimize the coefficients for the accuracy of the polynomial on the required range, but that experiment was unsuccessful.

It's all there in the repository, the implementations, notes about the different polynomials used, and the accuracy/speed statistics for the different methods.