Super interesting. Thank you.

You can't call it Ivy! That's an emacs package!

By definition, they can not be implemented. You can approximate them to some finite precision but you can not really implement them.

Damn, blogspot still exists! And it doesn't render well in my mobile, a product of simpler times.

Interesting reading about the difficulties with arctan.

There is a better series for arctan than the Taylor series which converges for all x. You can see it here in the accelerated series section

https://en.wikipedia.org/wiki/Arctangent_series

I wrote about it in my calculating pi blog some time ago

https://www.craig-wood.com/nick/articles/pi-machin/

It also takes fewer operations which is nice.

I thought it was invented by Euler but the Wikipedia article says Newton invented it and Euler popularized it.