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 ------------- Commit messages: - Update comments - Added parallelMultiply() method to BigInteger to allow large multiplications to run in parallel - Merge remote-tracking branch 'upstream/master' - Merge remote-tracking branch 'upstream/master' - Merge remote-tracking branch 'origin/master' - 8176501: Method Shape.getBounds2D() incorrectly includes Bezier control points in bounding box - 8176501: Method Shape.getBounds2D() incorrectly includes Bezier control points in bounding box Changes: https://git.openjdk.java.net/jdk/pull/6391/files Webrev: https://webrevs.openjdk.java.net/?repo=jdk&pr=6391&range=00 Issue: https://bugs.openjdk.java.net/browse/JDK-8277175 Stats: 731 lines in 8 files changed: 565 ins; 136 del; 30 mod Patch: https://git.openjdk.java.net/jdk/pull/6391.diff Fetch: git fetch https://git.openjdk.java.net/jdk pull/6391/head:pull/6391 PR: https://git.openjdk.java.net/jdk/pull/6391
