On Mon, 15 Nov 2021 15:50:39 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. > > > 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 This pull request has been closed without being integrated. ------------- PR: https://git.openjdk.java.net/jdk/pull/6391
