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Pi calculated to record 2.5 trillion digits

Anonymous Coward writes | more than 5 years ago

Supercomputing 6

Joshua writes "Researchers from Japan have calculated Pi to over 2.5 trillion decimals using the T2K Open Supercomputer (which is currently ranked 47th in the world according to a June, 2009 report from Top500.org). This new number more than doubles the previous record of about 1.2 trillion decimals set in 2002 by another Japanese research team. Unfortunately, there still seems to be no pattern."
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Stupid question... (1)

natehoy (1608657) | more than 5 years ago | (#29104053)

I know this is going to sound pretty stupid, but I'll ask anyway.

What do they calculate pi based on?

I mean, yes, I know it is used in the ratios between circle circumferences and volumes as compared to their diameters/radii, but how do you "calculate" extremely precise values of pi? What numbers go into the calculation and how are those numbers derived?

Do you draw a really frikkin huge circle and measure the circumference and diameter in atomic distances, or what?

Re:Stupid question... (1)

natehoy (1608657) | more than 5 years ago | (#29104097)

PS: Just looked it up on Wikipedia, and the answer they provided (using an n-sided polygon that approximates a circle and then increasing n to increase the correlation between the polygon and a circle) makes sense for approximations. I wonder what they had to crank "n" to on this computer to get this answer, assuming they used this method?

Re:Stupid question... (2, Informative)

eulernet (1132389) | more than 5 years ago | (#29105969)

Do you draw a really frikkin huge circle and measure the circumference and diameter in atomic distances, or what?

Yes, this is exactly how it's done. The circle is now the size of the universe.

Of course not, it's computed using mathematical formulas.
What is interesting is that there are two basically different methods to compute Pi.
http://mathworld.wolfram.com/PiFormulas.html [wolfram.com]

The first one is primarily based on Ramanujan's method. It's iterative and has a quadratic development, that means that you need one computer, and at each iteration, the number of correct decimals doubles.

The second one is based on Bailey and Borwein's method, with Plouffe's formula.
In short, you have a network of computers, and every computer can compute every decimal separately.

The japanese record has been set with the iterative method.
The main interest in such search is to improve multiprecision algorithms to compute numbers.
Computing very large numbers is done with the use of Fast Fourier Transform (FFT).

However, the network approach leads to unreachable records for a single computer.

I forgot to mention that the computation must be done TWICE with two different formulas to validate the computation.
IIRC, there is a known very fast formula for computing Pi on a single computer, and the second formula is much slower.

Re:Stupid question... (1)

Enter the Shoggoth (1362079) | more than 5 years ago | (#29106541)

In fact there's an interesting description of these algorithms on Fabrice Bellard's [bellard.org] site.

Extra geek points go to Fabrice as he is also the inventor of QEMU [nongnu.org] .

Re:Stupid question... (1)

TSchut (1314115) | more than 5 years ago | (#29116937)

Computing very large numbers is done with the use of Fast Fourier Transform (FFT).

Small correction: multiplying very large numbers is done with the use of the FFT, addition/subtraction not. That's because multiplication is very similar to convolution (try to multiply to numbers on paper and you'll see its pretty much the same as convolution of the numbers represented as arrays of digits), and convolution in the time domain is equal to pointwise multiplication in the frequency domain. For numbers with more than a certain amount of digits going through the FFT is actually faster. Furthermore I suppose you're referring to the Gauss-Legendre (http://en.wikipedia.org/wiki/Gaussâ"Legendre_algorithm) algorithm. Its difficulty is not in multiplication, because that can be done relatively fast using the FFT, but in the fact that there's a square root in it. If you approximate the square root wrong, this error will propagate through your iterations, so you must be very careful about that. Anyway, cool stuff!

Galactic-to-solar-system precision (1)

cfa22 (1594513) | more than 5 years ago | (#29114239)

Imagine the Milky Way as a disk with a circumference expressed, as usual, as 2*pi*R, where R is the radius. Having pi precise out to 10^12 digits means that the last significant digit measures distance on the order of a billion meters, or about 1/100th the distance between the Earth and the sun (since the radius of the Milky Way is about 5x10^20 meters [wikipedia.org] .
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