RFR: 8334755: Asymptotically faster implementation of square root algorithm [v21]

[Raffaello Giulietti]

On Tue, 2 Jul 2024 01:44:43 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:
> 
>   Ensure normalized value in MutableBigInteger initialization with ints

Everything not obvious that departs from the paper by Bertot, Magaud and Zimmermann should be commented.
Unfortunately, I can't say precisely what and to which extent until I see a first version.

-------------

PR Comment: https://git.openjdk.org/jdk/pull/19710#issuecomment-2218355974