On Wed, 15 Oct 2025 15:17:56 GMT, Raffaello Giulietti <[email protected]>
wrote:
>> @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.
>
> @fabioromano1 I think it is OK to have more efficient code even if the result
> is not correctly rounded.
> Please add some code comment about your error analysis.
@rgiulietti
> * How much code would be needed to attain correct rounding in all modes?
I found a way to make the procedure for correct rounding deterministic, but it
would complicate the code a lot, and of course it would be potentially
expensive in terms of running time, since the number of additional digits to
compute is finite but not bounded by a constant. So, if it were to be
implemented, the choice to have a correct rounding could be left to the user.
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PR Comment: https://git.openjdk.org/jdk/pull/27148#issuecomment-3418630905
