RFR: 8334755: Asymptotically faster implementation of square root algorithm [v50]

[Raffaello Giulietti]

On Thu, 1 Aug 2024 10:16:59 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> I have implemented the Zimmermann's square root algorithm, available in works [here](https://inria.hal.science/inria-00072854/en/) and [here](https://www.researchgate.net/publication/220532560_A_proof_of_GMP_square_root).
>> 
>> The algorithm is proved to be asymptotically faster than the Newton's Method, even for small numbers. To get an idea of how much the Newton's Method is slow,  consult my article [here](https://arxiv.org/abs/2406.07751), in which I compare Newton's Method with a version of classical square root algorithm that I implemented. After implementing Zimmermann's algorithm, it turns out that it is faster than my algorithm even for small numbers.
>
> fabioromano1 has updated the pull request incrementally with one additional commit since the last revision:
> 
>   Last small changes

I guess the overhead is negligible when compared to the arithmetic operation (shifts, divisions, etc.).
Also, the maximal stack depth for the recursion itself is quite limited and under control.
If at all, I would rather postpone that effort to a followup PR, and only if there are noticeable advantages without compromising readability.

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PR Comment: https://git.openjdk.org/jdk/pull/19710#issuecomment-2263781654