RFR: 8077587: BigInteger Roots [v23]

[fabioromano1]

On Mon, 14 Jul 2025 15:43:58 GMT, Raffaello Giulietti <rgiulietti at openjdk.org> wrote:

>> @rgiulietti The convergence of the recurrence is guaranteed if the initial estimate is larger than or equal to the exact value, AFAIK no guarantee is given when the estimate is smaller than the exact value.
>
> This is my hunch as well.
> So while the use of `nextUp()` and `ceil()` certainly help to achieve an overestimate, I'm less sure that this is sufficient when using `pow()`. If the latter has some error bigger than a few ulps, then we are in trouble.

@rgiulietti Now that I checked the recurrence better, it seems to me that it should give an overestimate if `rLong` is an underestimate, without modify it.

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PR Review Comment: https://git.openjdk.org/jdk/pull/24898#discussion_r2205358875