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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."
I didn't read the article, only the summery but it made me wonder.
Do they verify these numbers somehow?
Anyone can write down a series of a numbers and claim it's a specific sequence.
Not saying these numbers aren't correct, just a thought.
- Don't do what I do, it's probably not healthy nor safe. -
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.
Plain html is a wonderful thing. And as he points out, it would be easy to write a cgi script which returns a specified block of digits.
I wonder if he has checked for the circle?
http://michaelsmith.id.au
Core i7 clocking at 2.93GHz 6GB RAM 5 1.5TB Hard Drives (At least 7.2TB needed to store final result and base conversion)
He will be releasing the program he created for Windows (64bit only) and Linux
There is no -1 disagree
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$(205.5+RND(1)); : GOTO 10
Could someone fill me in what purpose that may be?
Because.
http://michaelsmith.id.au
He mentions in the "press release" page that the most important thing developed in his code is "an arbitrary-precision arithmetic library able to manipulate huge numbers stored on hard disks", which sounds basic-research-y. There's some more on that in the technical-details PDF, although unfortunately he says he doesn't plan to release the code (somewhat unusual, since most of his projects are free software).
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
There is an algorithm now for calculating the nth digit of Pi at a whim.
The algorithm only works for hexadecimal digits. There is no known formula or algorithm for calculating the n-th decimal digit directly.
Having said that, the existence or non-existence of an n-th digit algorithm does not have any relevance on the silliness or non-silliness of computing trillions of digits of pi, unless the algorithm is extremely trivial (i.e. computing the digit takes less CPU time than a byte of I/O), which is not the case here.
~Hal
What about this?
Basic research ..... you know that stuff that has no useful application now .....especially maths
Like group theory, invented in 1832 by Évariste Galois, had no really useful application until the mid 20th century ... Now quantum mechanics and so most of modern electronics uses it ....
Puteulanus fenestra mortis
It allows the unwashed masses (of which I am one) a chance to do things that were once only the realm of researchers in academia or the corporate world
I agree, that's why I have great hopes for my atomic bomb.
This is my sig.
in base pi. The answer was 10.
"To those who are overly cautious, everything is impossible. "