On Tue, 16 Nov 2021 13:22:46 GMT, kabutz <d...@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 <he...@javaspecialists.eu> Committer: Paul Sandoz <psan...@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 ------------- PR: https://git.openjdk.java.net/jdk/pull/6409
