RFR: JDK-8277175 : Add a parallel multiply method to BigInteger

[Kevin Rushforth]

On Mon, 15 Nov 2021 15:50:39 GMT, kabutz <duke at openjdk.java.net> wrote:

> BigInteger currently uses three different algorithms for multiply. The simple quadratic algorithm, then the slightly better Karatsuba if we exceed a bit count and then Toom Cook 3 once we go into the several thousands of bits. Since Toom Cook 3 is a recursive algorithm, it is trivial to parallelize it. I have demonstrated this several times in conference talks. In order to be consistent with other classes such as Arrays and Collection, I have added a parallelMultiply() method. Internally we have added a parameter to the private multiply method to indicate whether the calculation should be done in parallel.
> 
> The performance improvements are as should be expected. Fibonacci of 100 million (using a single-threaded Dijkstra's sum of squares version) completes in 9.2 seconds with the parallelMultiply() vs 25.3 seconds with the sequential multiply() method. This is on my 1-8-2 laptop. The final multiplications are with very large numbers, which then benefit from the parallelization of Toom-Cook 3.  Fibonacci 100 million is a 347084 bit number.
> 
> We have also parallelized the private square() method. Internally, the square() method defaults to be sequential.
> 
> 
> Benchmark                                          (n)  Mode  Cnt      Score      Error  Units
> BigIntegerParallelMultiply.multiply            1000000    ss    4     68,043 ±   25,317  ms/op
> BigIntegerParallelMultiply.multiply           10000000    ss    4   1073,095 ±  125,296  ms/op
> BigIntegerParallelMultiply.multiply          100000000    ss    4  25317,535 ± 5806,205  ms/op
> BigIntegerParallelMultiply.parallelMultiply    1000000    ss    4     56,552 ±   22,368  ms/op
> BigIntegerParallelMultiply.parallelMultiply   10000000    ss    4    536,193 ±   37,393  ms/op
> BigIntegerParallelMultiply.parallelMultiply  100000000    ss    4   9274,657 ±  826,197  ms/op

Additionally, you should probably discuss new functionality such as this on the appropriate mailing list, `core-libs-dev at openjdk.java.net` in this case.

Finally, this will need a CSR if it is to proceed.

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PR: https://git.openjdk.java.net/jdk/pull/6391