On Wed, 17 Nov 2021 19:48:25 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. >> >> Some benchmark results, run on my 1-6-2 server: >> >> >> Benchmark (n) Mode Cnt Score >> Error Units >> BigIntegerParallelMultiply.multiply 1000000 ss 4 51.707 >> ± 11.194 ms/op >> BigIntegerParallelMultiply.multiply 10000000 ss 4 988.302 >> ± 235.977 ms/op >> BigIntegerParallelMultiply.multiply 100000000 ss 4 24662.063 >> ± 1123.329 ms/op >> BigIntegerParallelMultiply.parallelMultiply 1000000 ss 4 49.337 >> ± 26.611 ms/op >> BigIntegerParallelMultiply.parallelMultiply 10000000 ss 4 527.560 >> ± 268.903 ms/op >> BigIntegerParallelMultiply.parallelMultiply 100000000 ss 4 9076.551 >> ± 1899.444 ms/op >> >> >> We can see that for larger calculations (fib 100m), the execution is 2.7x >> faster in parallel. For medium size (fib 10m) it is 1.873x faster. And for >> small (fib 1m) it is roughly the same. Considering that the fibonacci >> algorithm that we used was in itself sequential, and that the last 3 >> calculations would dominate, 2.7x faster should probably be considered quite >> good on a 1-6-2 machine. > > kabutz has updated the pull request incrementally with one additional commit > since the last revision: > > Removed JVM flags from benchmark To add my 2c IMO a parallel version of this type absolutely **must** be opt-in. There are simply far too many side-effects of using the FJP and multiple threads to perform the calculation in parallel as if it is just a minor implementation detail. A clear API is 1000x better than a "kill switch". And yes you may still need to expose some kind of tuning knob. David ------------- PR: https://git.openjdk.java.net/jdk/pull/6409
