That paper was concerned with doubles and getting the initial approximation to slightly under 8 bits was sufficient to get a correctly rounded double sqrt within 3 iterations.
Tweaking the magic valu...
Although the original thing never got published, a different paper analyzing the algorithm (and confirming it gives correctly rounded results) was, in 1992: https://bpb-us-e1.wpmucdn.com/websites.uta.edu/dist/7/5059/files/2021/06/csd-94-850.pdf
it also gives more of an explanation why it works, the original Kahan/Ng paper just assumes you're familiar with how IEEE floats are constructed and expects you to keep up. :)
it also gives more of an explanation why it works, the original Kahan/Ng paper just assumes you're familiar with how IEEE floats are constructed and expects you to keep up. :)
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