RFR: 8077587: BigInteger Roots [v23]

[Raffaello Giulietti]

On Mon, 14 Jul 2025 16:41:15 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> 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.

Can you please provide a succinct "proof" in form of a comment? Needs to be convincing, although not necessarily rigorous.

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PR Review Comment: https://git.openjdk.org/jdk/pull/24898#discussion_r2226184420