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

[kabutz]

On Tue, 16 Nov 2021 13:22:46 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.
> 
> Some benchmark results, run on my 1-6-2 server:
> 
> 
> Benchmark                                          (n)  Mode  Cnt      Score      Error  Units
> BigIntegerParallelMultiply.multiply            1000000    ss    4     51.707 ±   11.194  ms/op
> BigIntegerParallelMultiply.multiply           10000000    ss    4    988.302 ±  235.977  ms/op
> BigIntegerParallelMultiply.multiply          100000000    ss    4  24662.063 ± 1123.329  ms/op
> BigIntegerParallelMultiply.parallelMultiply    1000000    ss    4     49.337 ±   26.611  ms/op
> BigIntegerParallelMultiply.parallelMultiply   10000000    ss    4    527.560 ±  268.903  ms/op
> BigIntegerParallelMultiply.parallelMultiply  100000000    ss    4   9076.551 ± 1899.444  ms/op
> 
> 
> We can see that for larger calculations (fib 100m), the execution is 2.7x faster in parallel. For medium size (fib 10m) it is 1.873x faster. And for small (fib 1m) it is roughly the same. Considering that the fibonacci algorithm that we used was in itself sequential, and that the last 3 calculations would dominate, 2.7x faster should probably be considered quite good on a 1-6-2 machine.

This pull request has now been integrated.

Changeset: 83ffbd2e
Author:    Dr Heinz M. Kabutz <heinz at javaspecialists.eu>
Committer: Paul Sandoz <psandoz at openjdk.org>
URL:       https://git.openjdk.java.net/jdk/commit/83ffbd2e7aed8a9c788395ccbe920ddff221ae16
Stats:     601 lines in 4 files changed: 582 ins; 0 del; 19 mod

8277175: Add a parallel multiply method to BigInteger

Reviewed-by: psandoz

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PR: https://git.openjdk.java.net/jdk/pull/6409