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Supercomputing

+ - Pi calculated to record 2.5 trillion digits-> 6

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Joshua
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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Pi calculated to record 2.5 trillion digits

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  • 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?

    • by natehoy (1608657)

      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: (Score:3, Informative)

      by eulernet (1132389)

      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 Borwe

      • 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].

      • by TSchut (1314115)

        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. Furtherm

  • 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].

How can you work when the system's so crowded?

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