[gambit-list] Computing a billion decimal digits of pi

Hendrik Boom hendrik at topoi.pooq.com
Wed Jul 10 14:28:48 EDT 2013


On Wed, Jul 10, 2013 at 11:47:48AM -0400, Bradley Lucier wrote:
> On 06/12/2013 01:07 PM, Bradley Lucier wrote:
> >
> > Just for laughs and giggles, I decided to calculate 1,000,000,000 
> > (yes, 9 zeros) digits of pi using Bakul Shah's Scheme program 
> > implementing the Chudnovsky algorithm.  The computation used one CPU 
> > core:
> >
> > model name    : Intel(R) Xeon(R) CPU           X5570  @ 2.93GHz
> >
> > with a pretty good memory subsystem with 72GB of memory ...
> >
> > leibniz-172% gsi chud2
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 10, CPU time: 0..
> > Last 5 digits 26535.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 100, CPU time: 0..
> > Last 5 digits 70679.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 1000, CPU time: 0..
> > Last 5 digits 1989.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 10000, CPU time: .020000000000000004.
> > Last 5 digits 75678.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 100000, CPU time: .340022.
> > Last 5 digits 24646.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 1000000, CPU time: 5.140321.
> > Last 5 digits 58151.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 10000000, CPU time: 83.765235.
> > Last 5 digits 55897.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 100000000, CPU time: 1327.790981.
> > Last 5 digits 51592.
> > Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> > 1000000000, CPU time: 41907.731069.
> > Last 5 digits 45519.
> >
> 
> This is the same program, run on my new desktop:
> 
> model name    : Intel(R) Core(TM) i7-4770 CPU @ 3.40GHz
> 
> with 16GB of RAM, which seems to run 2-3 times as fast as the server in 
> the math department.  (Luckily, a new server will be up and running soon.)
> 
> Brad
> 
> firefly:~/programs/gambiteer> gsi chud2
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 10, CPU time: 0..
> Last 5 digits 26535.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 100, CPU time: 0..
> Last 5 digits 70679.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 1000, CPU time: 0..
> Last 5 digits 1989.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 10000, CPU time: .012.
> Last 5 digits 75678.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 100000, CPU time: .172.
> Last 5 digits 24646.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 1000000, CPU time: 2.476.
> Last 5 digits 58151.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 10000000, CPU time: 38.7.
> Last 5 digits 55897.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 100000000, CPU time: 536.864.
> Last 5 digits 51592.
> Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 
> 1000000000, CPU time: 14459.672.
> Last 5 digits 45519.

I'm an old-timer.  I remember in the 60's when someone had calculated 
the first million digits off pi and offered to sell them on a reel of 
magnetic tape.

I was impressed.  Though not having a magnetic tape reader, and not 
needing more than the first five or so digits, I didn't take 
up the offer.

Thhe did say they hadn't found seven consecutive 7's in those million 
digits, though.

Is it now faster to calculate them than to download them?

-- hendrik



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