RFR: 8341470: BigDecimal.stripTrailingZeros() optimization [v42]

[fabioromano1]

On Sun, 13 Oct 2024 16:34:09 GMT, Raffaello Giulietti <rgiulietti at openjdk.org> wrote:

>>> What's really crucial for _correctness_ is to ensure maxPowsOf5 >= k.
>> 
>> Yes, I meant that the only way we know to ensure that condition is to ensure `m <= maxPowsOf5`...
>> 
>>> Perhaps leave m <= maxPowsOf5 <= m + 1 and maxPowsOf5 >= k and drop the note "and is never off by more than 1 from the theoretical m"
>> 
>> I would put `maxPowsOf5 <= m + 2` instead, because `maxPowsOf5 <= m + 1` is not obvious to prove mathematically...
>
> It can be proven by considering
> 
> - the inequality | b * LOG_5_OF_2 - b log5(2) | < 2^(-21)
> - the properties of round() (to an integer)
> - log5(2) < 1/2
> 
> The last one is crucial for the upper bound to be m + 1 rather than m + 2.
> 
> Feel free to use m + 2, though.

I understood that it follows from the fact that `log5(2^(n+1)) - log5(2^n) == [log5(2^n) + log5(2)] - log5(2^n)`, but I think it's superfluous having to explain it in the comments just to prove `maxPowsOf5 <= m + 1`, while it is more clear to understand why `maxPowsOf5 <= m + 2` is true. Anyway, thanks for the insight.

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PR Review Comment: https://git.openjdk.org/jdk/pull/21323#discussion_r1798459950