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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