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I wonder how does it compare with Microsoft’s implementation, there: https://github.com/microsoft/DirectXMath/blob/jan2021/Inc/Di...
Based on the code your version is probably much faster. It would be interesting to compare precision still, MS uses 17-degree polynomial there.
Indeed, degree-4 rational polynomials are generally enough for JPEG XL. Code for evaluating them using Horner's scheme (just FMAs): https://github.com/libjxl/libjxl/blob/bdde644b94c125a15e532b...
I initially used Chebfun to approximate them, then a teammate implemented the same Caratheodory-Fejer method in C. We subsequently convert from Chebyshev basis to monomials.
Blog sounds good :)
(I'm the author)
You're right, I should have specified -- it is glibc 2.32-48 . This the source specifying how glibc is built: https://github.com/NixOS/nixpkgs/blob/97c5d0cbe76901da0135b0... .
I've amended the article so that it says `glibc` rather than `libc`, and added a sidenote specifying the version.
I link to it statically as indicated in the gist, although I believe that shouldn't matter. Also see https://gist.github.com/bitonic/d0f5a0a44e37d4f0be03d34d47ac... .
Note that the hardware is not particularly recent (Q3 2017), but we tend to rent servers which are not exactly on the bleeding edge, so that was my platform.
The sin(x) = x approximation is exact (in terms of doubles) for x < 2^-26 = 1.4e-8. See also https://github.com/lattera/glibc/blob/master/sysdeps/ieee754....
