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CORDIC is a well-known method for quickly computing exponentials and logs, including trig functions and their inverses by decomposing the angle into conveniently computable increments and then repeatedly applying the rotation increments in such a way to approximate the desired angle.

What is less well-known is that it can compute far more general special functions by considering an extension to more general Lie groups. It is apparently possible to evaluate multi-parameter functions like the Bessel functions by considering their properties: http://ieeexplore.ieee.org/document/1171404/ but this paper is short on details.

I haven't seen any modern treatment of the CORDIC from the group theoretical perspective. Is there a clearly documented way to derive the algorithms for an arbitrary Lie group?

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  • $\begingroup$ This is intensely interesting, but I won't have time to read into the numerics of it. Seeing this is rather niche from an electrical engineering and signal processing perspective, maybe IEEExplore is not the most important source of information on these things. You might need to go and take the parts of CORDIC and research them in a numerical math rather than a signal processing context, is a gut feeling that I get. $\endgroup$
    – Marcus Müller
    Commented Jul 13, 2023 at 9:06
  • $\begingroup$ Unfortunately that is the only paper I can find that even mentions the link. IEEE handles a lot of numerical computing for what's it's worth, and dsp is just numerics in the end. $\endgroup$
    – nimish
    Commented Jul 14, 2023 at 19:47

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