RFR: JDK-8277175 : Add a parallel multiply method to BigInteger [v3]

[kabutz]

> 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 15 additional commits since the last revision:

 - 8277119: Add asserts in GenericTaskQueueSet methods
   
   Reviewed-by: tschatzl
 - 8274757: Cleanup unnecessary calls to Throwable.initCause() in java.management module
   
   Reviewed-by: dfuchs, sspitsyn
 - 8274662: Replace 'while' cycles with iterator with enhanced-for in jdk.hotspot.agent
   
   Reviewed-by: amenkov, cjplummer, sspitsyn
 - 8274163: Use String.equals instead of String.compareTo in jdk.jcmd
   
   Reviewed-by: cjplummer, amenkov, sspitsyn
 - 8274190: Use String.equals instead of String.compareTo in jdk.internal.jvmstat
   
   Reviewed-by: cjplummer, sspitsyn
 - 8274168: Avoid String.compareTo == 0 to check String equality in java.management
   
   Reviewed-by: sspitsyn, dfuchs, cjplummer, dholmes
 - 8274261: Use enhanced-for instead of plain 'for' in jdk.jcmd
   
   Reviewed-by: sspitsyn, cjplummer
 - Update comments
 - Added parallelMultiply() method to BigInteger to allow large multiplications to run in parallel
 - Merge branch 'openjdk:master' into master
 - ... and 5 more: https://git.openjdk.java.net/jdk/compare/744e9e8e...0075f04d

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Changes:
  - all: https://git.openjdk.java.net/jdk/pull/6391/files
  - new: https://git.openjdk.java.net/jdk/pull/6391/files/03be5518..0075f04d

Webrevs:
 - full: https://webrevs.openjdk.java.net/?repo=jdk&pr=6391&range=02
 - incr: https://webrevs.openjdk.java.net/?repo=jdk&pr=6391&range=01-02

  Stats: 0 lines in 0 files changed: 0 ins; 0 del; 0 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