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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. -
But will it help us in getting flying cars?
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
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.
speeding bullet, and was able to leap tall buildings in a single bound. Fabrice needs to lift his game.
The Internet's nature is peer to peer - 20050301_cs_profs.pdf
Exactly! And hence the discovery of our blessed lady of the grilled cheese sandwich...
Read... The... Fine... (wait for it) Article!
Spoiler alert!
He developed a highly efficient library for arbitrary precision floating-point number calculations, capable of having a desktop machine best a supercomputer. Now go change your signature to "For lack of a better question..." ;-)
"The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again."
Depends on what you mean by "pattern", of course, but pi is conjectured to be normal, which would exclude many sorts of patterns. It's not proven, though.
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
~Hal
Knowing how to calculate the nth digit of Pi itself is slightly retarded.
The observable universe is about 50 billion light years across, which is about 4.27 * 10^26 meters. If we take a ring of atoms each roughly 1 Angstrom (10^-10 meters) apart with a diameter the size of the observable universe and want to determine the circumference of the resulting circle, then knowing Pi to 40 or so places is sufficient that the error caused by the atoms themselves is greater than that introduced by using an approximate value for Pi. Knowing Pi to 40 or so places is sufficient that you can calculate the difference in circumferences of the inner diameter of the ring and outer diameter of the ring.
Knowing Pi to 40 places is basically sufficient for describing our entire universe and anything you could put into it. We've known the first 35 for four hundred years, and we've never needed that much information to describe our universe.
The road to tyranny has always been paved with claims of necessity.
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
I don't think many people will be running his program that takes 116 days to complete to get as far as he did. Would have been nice to at least see how the code worked.
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.
Well given (I think, though may be wrong on this) that pretty much any finite sequence of digits will show up in the decimal expansion of pi at some point, there should be a raster image of a circle in 1s and 0s buried in it somewhere. Along with a greyscale raster of Goatse.
in base pi. The answer was 10.
"To those who are overly cautious, everything is impossible. "
In any large enough collection of random numbers you will be guaranteed to find whatever pattern you're looking for, whether it's a hundred thousand zeros in a row or the text of the collected works of Shakespeare. You can test statistically how likely you are to find particular patterns in a collection of numbers of a particular size though.
Finding patterns can be hard. If you have an idea of what you're looking for you can do much better than if you just want to find any pattern. SETI at Home has a page about what they look for: http://seticlassic.ssl.berkeley.edu/about_seti/about_seti_at_home_4.html
Fabrice Bellard continues to amaze me.
What about this?
The algorithm you linked to requires cubic time in n. It hardly qualifies as "calculating the n-th decimal digit directly" given that the naive approach (calculating every single digit between 1 and n, and throwing away all but the last digit) is faster than cubic time.
The only advantage of the algorithm you linked to is that it requires constant space.
Angstroms are awful big. Just for the sake of maximum precision, how many digits would you need if you were measuring in planck lengths?