RFR: 8366478: BigDecimal roots

[fabioromano1]

On Wed, 15 Oct 2025 10:10:43 GMT, Raffaello Giulietti <rgiulietti at openjdk.org> wrote:

>> @rgiulietti Here is the PR.
>
> @fabioromano1 In the comments there are claims about the relative errors. Two questions arise:
> * How were the bounds determined? There seems to be no indication in the comments provided so far.
> * How much code would be needed to attain correct rounding in all modes?

@rgiulietti 
> * How much code would be needed to attain correct rounding in all modes?

The best that can be done is to make the probability of an incorrect rounding as small as desired, but this can be computationally expensive: a probability within $10^{-k}$ means that the integer root must have $k$ more digits, and so the radicand must have $n \cdot k$ more digits.

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PR Comment: https://git.openjdk.org/jdk/pull/27148#issuecomment-3406716684