[gambit-list] Computing pi with parallel gambit
Bradley Lucier
lucier at math.purdue.edu
Fri Dec 9 11:21:52 EST 2016
On 11/28/2016 10:56 AM, Marc Feeley wrote:
> Yes parallelizing Karatsuba multiplication should be very easy. That will make an interesting experiment when the multiple threaded VM configuration is stable. I expect very close to linear speedup given the independent sub-multiplications.
The Chudnovsky algorithm for $\pi$ is implemented using binary splitting
of a series, and the independent sub-series can also be computed in
parallel and then combined. This parallelism can be exploited even for
not-so-large numbers of digits.
You get about 14 digits accuracy per term in the series, so for a
billion digits you'd need about 70 million terms.
It'd be interesting to see how much overhead one incurs in distributing
this computation to several processes. I imagine that processing 10,000
to 100,000 terms in a single process might be a good cutoff point, but
we'd have to see.
Brad
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