> 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
kabutz has updated the pull request with a new target base due to a merge or a rebase. The incremental webrev excludes the unrelated changes brought in by the merge/rebase. The pull request contains eight additional commits since the last revision: - Merge branch 'openjdk:master' into parallel-bigInteger - 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 Addressing some of Laurent's code review recommendations/comments: 1. use the convention t for the parametric variable x(t),y(t) 2. solve the quadratic equation using QuadCurve2d.solveQuadratic() or like Helpers.quadraticRoots() 3. always use braces for x = (a < b) ? ... 4. always use double-precision constants in math or logical operations: (2 * x => 2.0 * x) and (coefficients[3] != 0) => (coefficients[3] != 0.0) (There are two additional recommendations not in this commit that I'll ask about shortly.) See https://github.com/openjdk/jdk/pull/6227#issuecomment-959757954 - 8176501: Method Shape.getBounds2D() incorrectly includes Bezier control points in bounding box The bug writeup indicated they wanted Path2D#getBounds2D() to be more accurate/concise. They didn't explicitly say they wanted CubicCurve2D and QuadCurve2D to become more accurate too. But a preexisting unit test failed when Path2D#getBounds2D() was updated and those other classes weren't. At this point I considered either: A. Updating CubicCurve2D and QuadCurve2D to use the new more accurate getBounds2D() or B. Updating the unit test to forgive the discrepancy. I chose A. Which might technically be seen as scope creep, but it feels like a more holistic/better approach. This also includes a new unit test (in Path2D/UnitTest.java) that fails without the changes in this commit. ------------- Changes: - all: https://git.openjdk.java.net/jdk/pull/6391/files - new: https://git.openjdk.java.net/jdk/pull/6391/files/eac09f15..03be5518 Webrevs: - full: https://webrevs.openjdk.java.net/?repo=jdk&pr=6391&range=01 - incr: https://webrevs.openjdk.java.net/?repo=jdk&pr=6391&range=00-01 Stats: 24162 lines in 218 files changed: 17701 ins; 2440 del; 4021 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
