RFR: 8334755: Asymptotically faster implementation of square root algorithm [v34]

[Raffaello Giulietti]

On Thu, 18 Jul 2024 17:22:50 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:
> 
>   Conditions' order reversed in MBI.ulongSqrt()

AFAIU, the wrapper performs the normalization, invokes the core algorithm, and does the denormalization just before returning the final result. There's no mention that normalization/denormalization need to be performed at each recursive call.
The C code in §5.1 assumes a normalized input and, as far as I can see, does not perform any denormalization.

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

PR Comment: https://git.openjdk.org/jdk/pull/19710#issuecomment-2245535146