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

[Raffaello Giulietti]

On Sun, 13 Oct 2024 16:18:03 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> 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"
>
>> 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.

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PR Review Comment: https://git.openjdk.org/jdk/pull/21323#discussion_r1798446904