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

[Raffaello Giulietti]

On Sun, 13 Oct 2024 16:57:33 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> 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.

With the notation above, the reasoning goes like so:

2^(b-1) <= v < 5^(m+1), hence b log5(2) < m + 1 + log5(2).
This implies b * LOG_5_OF_2 < m + 1 + log5(2) + 2^(-21) < m + 1 + 1/2,
which leads to round(b * LOG_5_OF_2) <= m + 1.

As said, I don't mind if you prefer m + 2.

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PR Review Comment: https://git.openjdk.org/jdk/pull/21323#discussion_r1798522972