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

[Paul Sandoz]

On Fri, 19 Nov 2021 10:42:23 GMT, kabutz <duke at openjdk.java.net> wrote:

> > I think the functionality in this PR is worth pursuing, but with the JDK 18 rampdown 1 date fast approaching, as a non-urgent issue, I think we shouldn't try to rush it into JDK 18.
> 
> > I looked more closely and now understand a bit more about the threshold. It would be useful to have some implementation notes detailing approximately when the parallel execution kicks in. For `a*a` it's `>= TOOM_COOK_SQUARE_THRESHOLD(216)` and for `a*b` it's `>= TOOM_COOK_THRESHOLD(240)`, so we could refer to certain bit lengths.
> > The branching factor is 4 (well 3 i guess, but its easier to think in powers of 2). It might be reasonable to assume the problem gets split equally in 4 parts. I don't know in practice what the depth of recursion might, its hard to see this getting completely out of control, but we could always keep track of the depth and cut off in proportion to the # runtime processors if need be.
> > Given the existing degree of specialization, the minimal changes to code, and the fact that the creation of recursive tasks is in the noise this PR looks quite reasonable.
> 
> I have run some more tests. For my fibonacci algorithm, here are the worst cases for the various calculations.
> 
> ```
>             n   most_bits     tasks  time_ms
>          1000         694         0      1
>        10_000       6_942         0      1
>       100_000      69_424        18     13
>     1_000_000     694_241       468    143
>    10_000_000   6_942_418    11_718   1049
>   100_000_000  69_424_191   292_968  13695
> 1_000_000_000 694_241_913 7_324_218 237282
> ```
> 
> Each data point has 10x the number of bits in the final result and the number of tasks in the final calculation is 25x more. Perhaps I can make the threshold the recursive depth up to which we would run in parallel. And that recursive depth could the availableProcessors() or some multiple thereof.
> 

Defense in depth :-) Perhaps a depth that is between some multiple of log2 and log4 of `availableProcessors()`, given the branching factor.

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PR: https://git.openjdk.java.net/jdk/pull/6409