RFR: 8077587: BigInteger Roots [v2]

[fabioromano1]

On Wed, 16 Apr 2025 22:05:34 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> This PR implements nth root computation for `BigInteger`s using Newton method and optimizes `BigInteger.pow(int)` method.
>> [Here is a proof of convergence of the recurrence used.](https://github.com/user-attachments/files/19785045/nth_root_newton_proof_integers.pdf)
>
> fabioromano1 has updated the pull request incrementally with one additional commit since the last revision:
> 
>   Correct loop recurrence according to proof of convergence

@rgiulietti In this PR I've implemented nth root for BigIntegers using Newton's method and optimized BigInteger.pow(int) method. I've also uploaded a proof of convergence for the recurrence used to compute nth root.

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PR Comment: https://git.openjdk.org/jdk/pull/24690#issuecomment-2810926459