RFR: 8341470: BigDecimal.stripTrailingZeros() optimization [v44]

[Raffaello Giulietti]

On Tue, 15 Oct 2024 09:02:58 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> While I intuitively understand, and I'm convinced of the clever algorithm, I'm struggling to find a proof, in particular to formulate a useful invariant for the first loop which seamlessly would bind with the second loop and its invariant.
>> I need to find more time for this.
>
> @rgiulietti Actually, an useful invariant for `remainingZeros` follows directly from its definition: letting `z = max{n : ((intVal * 2^powsOf2) % 10^n) == 0 && n <= scale - preferredScale}`, at the first iteration, it is true that `remainingZeros >= z`, and the loop condition is `remainingZeros >= 2^i`. So, if `z < 2^i`, then `intVal % 5^(2^i) != 0` and the "then" branch of the "if" is executed, otherwise `z >= 2^i` and the "else" branch is executed. In both branches, the invariant `remainingZeros >= z` is preserved by the instructions.

Yes, I considered that as well.
Not sure, however, if this is sufficient to prove that intVal has been indeed divided by 5^z after the 2nd loop is terminated.

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PR Review Comment: https://git.openjdk.org/jdk/pull/21323#discussion_r1800761892