On Tue, 16 Nov 2021 12:48:03 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 > > kabutz has updated the pull request with a new target base due to a merge or > a rebase. The pull request now contains four commits: > > - Update comments > - Added parallelMultiply() method to BigInteger to allow large > multiplications to run in parallel > - 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. Resubmitted as PR https://github.com/openjdk/jdk/pull/6409/ ------------- PR: https://git.openjdk.java.net/jdk/pull/6391
