[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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