On Thu, 16 Dec 2021 06:07:29 GMT, kabutz <[email protected]> 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:
>
> Changed depth type to byte to save 8 bytes on each RecursiveSquare instance
test/jdk/java/math/BigInteger/BigIntegerParallelMultiplyTest.java line 64:
> 62: BigInteger fib = fibonacci(n, BigInteger::multiply);
> 63: System.out.printf("fibonacci(%d) = %d%n", n, fib);
> 64: }
I think we can remove this and the loop block at #70-80, since we have the
performance test. After that we are good.
-------------
PR: https://git.openjdk.java.net/jdk/pull/6409
