RFR: 4837946: Faster multiplication and exponentiation of large integers [v34]

[Chen Liang]

On Sat, 26 Apr 2025 16:44:26 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> This PR optimizes `BigInteger.pow(int)` method. The primary enhancement in `pow()` is not concerned most on execution time, but rather in memory optimization, because the PR implementation does the "shift of the exponent" squaring the result rather than the base, so the base is not squared like in the current implementation, and this permits to save about half of the memory.
>
> fabioromano1 has updated the pull request incrementally with one additional commit since the last revision:
> 
>   Removed  method used by nth-root

src/java.base/share/classes/java/math/BigInteger.java line 2721:

> 2719:             if (!pow.equals(ONE)) {
> 2720:                 for (int i = 0; i < blockLen; i++)
> 2721:                     pow = pow.multiply(pow);

Majority of the time we have `blockLen == maxExpLen`. We should cache that pow-to-maxExpLen result too, if we have `maxExpLen >= nLen` initially. Maybe also calculate power-to-`nLen % maxExpLen` as that will be used in the final round of the loop.

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PR Review Comment: https://git.openjdk.org/jdk/pull/24690#discussion_r2061496813