In physics grad school, professors would occasionally allude to it, and textbooks would cite it ... pretty often. So it's a thing anyone with postgraduate physics education should know exists, but you wouldn't ever be assigned it.
For my undergrad the CRC math handbook was enough.
And, lo and behold, the ASIN implementation is minimax.
The SLEEF Vectorized Math Library [1] does this and therefore can usually provide accuracy guarantees for the whole floating point range with a polynomial order lower than theory would predict.
Its asinf function [2] is accurate to 1 ULP for all single precision floats, and is similar to the `asin_cg` from the article, with the main difference the sqrt is done on the input of the polynomial instead of the output.
[1] https://sleef.org/ [2] https://github.com/shibatch/sleef/blob/master/src/libm/sleef...
> This amazing snippet of code was languishing in the docs of dead software, which in turn the original formula was scrawled away in a math textbook from the 60s.
was kind of telling for me. I have some background in this sort of work (and long ago concluded that there was pretty much nothing you can do to improve on existing code, unless either you have some new specific hardware or domain constraint, or you're just looking for something quick-n-dirty for whatever reason, or are willing to invest research-paper levels of time and effort) and to think that someone would call Abramowitz and Stegun "a math textbook from the 60s" is kind of funny. It's got a similar level of importance to its field as Knuth's Art of Computer Programming or stuff like that. It's not an obscure text. Yeah, you might forget what all is in it if you don't use it often, but you'd go "oh, of course that would be in there, wouldn't it...."