Implementing Cosine in C from Scratch (2020)
The implementation of the __cos kernel in Musl is actually quite elegant. After reducing the input to the range [-pi/4, pi/4], it just applies the best degree-14 polynomial for approximating the cosine on this interval. It turns out that this suffices for having an error that is less than the machine precision. The coefficients of this polynomial can be computed with the Remez algorithm, but even truncating the Chebyshev expansion is going to yield much better results than any of the methods proposed by the author.