RFR: 8334755: Asymptotically faster implementation of square root algorithm [v9]

[Daniel Jeliński]

On Sun, 23 Jun 2024 19:03:38 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:
> 
>   Code optimization

Thanks. That's a very nice performance improvement, on my Windows machine the `testHuge...` test is about 2-3x faster, and the other 2 are slightly faster too.

This needs a proper review for correctness, which might take a while.

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PR Comment: https://git.openjdk.org/jdk/pull/19710#issuecomment-2187034545