Can you produce a version that isn't limited by floating point? I was trawling the research papers as usual and found a particularly simple and novel way of finding sqrts (its not the Babylonian way!), so I decided to implement it in scratch. As with many algorithms, this one runs into 16 bit floating point issues, though I am sure this could be easily over come given the non decimal nature of the algorithm and the simplicity of its construction. Anyways check out the paper and look inside to see how it works!
All the wonderful people who worked to make this paper possible: https://arxiv.org/html/2312.15338v1 Especially Mayer Goldberg who appears to have been to one to write/publish it.