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New Pi Computation Record Using a Desktop PC
hint3 writes "Fabrice Bellard has calculated Pi to about 2.7 trillion decimal digits, besting the previous record by over 120 billion digits. While the improvement may seem small, it is an outstanding achievement because only a single desktop PC, costing less than $3,000, was used — instead of a multi-million dollar supercomputer as in the previous records."
From the FAQ
"How does your record compares to the previous one ?
The previous Pi computation record of about 2577 billion decimal digits was published by Daisuke Takahashi on August 17th 2009. The main computation lasted 29 hours and used 640 nodes of a T2K Open Supercomputer (Appro Xtreme-X3 Server). Each node contains 4 Opteron Quad Core CPUs at 2.3 GHz, giving a peak processing power of 94.2 Tflops (trillion floating point operations per second).
My computation used a single Core i7 Quad Core CPU at 2.93 GHz giving a peak processing power of 46.9 Gflops. So the supercomputer is about 2000 times faster than my computer. However, my computation lasted 116 days, which is 96 times slower than the supercomputer for about the same number of digits. So my computation is roughly 20 times more efficient. It can be explained by the following facts:
* The Pi computation is I/O bound, so it needs very high communication speed between the nodes on a parallel supercomputer. So the full power of the supercomputer cannot really be used.
* The algorithm I used (Chudnovsky series evaluated using the binary splitting algorithm) is asymptotically slower than the Arithmetic-Geometric Mean algorithm used by Daisuke Takahashi, but it makes a more efficient use of the various CPU caches, so in practice it can be faster. Moreover, some mathematical tricks were used to speed up the binary splitting. " ( http://bellard.org/pi/pi2700e9/faq.html )
Mathematical and Programming Ownage.
Now I can finally get somewhat reasonable precision when calculating the radius of stuff!
For those not previously familiar with Fabrice Bellard, he's known for:
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
Only if you avoid the square routes.
1 TB data files... somebody needs to help him with the compression! Oh, wait a minute.
As he points out himself, he doesn't really care about calculating digits of Pi; it's a convenient hook on which to hang an interesting algorithms challenge. From the FAQ:
He also mentions elsewhere that of his code, "The most important part is an arbitrary-precision arithmetic library able to manipulate huge numbers stored on hard disks."
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
~Hal