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Math Australia IBM Supercomputing Science

Blue Gene/P Reaches Sixty-Trillionth of Pi Squared 212

Posted by timothy
from the just-warming-it-up dept.
Reader Dr.Who notes that an Australian research team using IBM's Blue Gene/P supercomputer has calculated the sixty-trillionth binary digit of Pi-squared, a task which took several months of processing. Snipping from the article, the Dr. writes: "'A value of Pi to 40 digits would be more than enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton.' The article goes on to cite use of computationally complex algorithms to detect errors in computer hardware. The article references a blog which has more background. Disclaimers: I attended graduate school at U.C. Berkeley. I am presently employed by a software company that sells an infrastructure product named PI."
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Blue Gene/P Reaches Sixty-Trillionth of Pi Squared

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  • by garcia (6573) on Saturday April 30, 2011 @08:13PM (#35987620) Homepage

    From the blurb:

    Disclaimers: I attended graduate school at U.C. Berkeley. I am presently employed by a software company that sells an infrastructure product named PI.

    Oh, I expected the sentence to end with, "...and I still don't know why the fuck anyone cares about a number this long."

    I'm going to the bar. Who's with me?

    • by kenj0418 (230916)

      Well, I'm going to Pi. http://www.restaurantpi.com/ [restaurantpi.com]

    • by chebucto (992517)

      why the fuck anyone cares about a number this long

      Seriously, does anyone have an answer for this? Unless they're waiting to see if the digits start repeating themselves, I don't get why anyone would need a value of pi to be so precise.

      Personally, I've assumed that the stupidly-precise values of pi were calculated out of pure obsessiveness and, perhaps, a desire for fame (of a kind).

      But if they're using months of time on a very expensive, very new, publicly-funded supercomputer to calculate the value, then there's _got_ to be a reason. Right?

      • by chebucto (992517)

        After waiting minutes for an answer, I decided to RTFA and, well, there is a reason (or at least a good excuse)

        one application for computing the digits of Pi is to test the integrity of computer hardware and software, which is a focus of Baileyâ(TM)s research at Berkeley Lab. âoeIf two separate computations of digits of Pi, say using different algorithms, are in agreement except perhaps for a few trailing digits at the end, then almost certainly both computers performed trillions of operations flawlessy"

        • by gfody (514448)
          I don't buy it. Trillions of operations later we know the Sixty-trillionth binary digit of pi squared is 1 and the hardware is flawless or 50/50 chance it got lucky
          • I don't buy it. Trillions of operations later we know the Sixty-trillionth binary digit of pi squared is 1 and the hardware is flawless or 50/50 chance it got lucky

            Fifty-fifty, huh?

          • Well, presumably they compare strings of digits. But yeah, the article is less than clear.
      • by statusbar (314703)

        They are secretly looking for the digits to form an infinite series of encoded bitmaps of a circles, in order to prove that god has a sense of humour.

        --jeffk++

      • why the fuck anyone cares about a number this long

        Because... if we have more binary digits of Pi, we can search for subsequences of digits representing mp3 songs. Using that, we can show that RIAA is wrong, because as a matter of fact, you can't copyright mathematics.

      • This reminds me of an altercation on one of the newsgroups a few years back, and I quote:

        > > In article eugene@ames.UUCP (Eugene Miya) writes:
        > > >We have just received a letter from Japan that a newer record for
        > > >computation of digits of Pi was accomplished. Previously David Bailey
        > > >here at Ames did a 30 million digit computation on the Cray-2.
        > > >The new computation was done on an older Hitachi 810 supercomputer
        > > >using extended storage. The n

  • What does that number "do"?

    Pi is famous, and the more well known number to crunch. Why crunch Pi Squared? Can't you just square Pi?

    • by MoonBuggy (611105)

      Can't you just square Pi?

      Well, yes, but doing so to vast precision requires you to to crunch a vast number of digits of pi, so I imagine it's all largely the same in the end.

      • by superwiz (655733)
        Yep. Squaring a number is an O(n^2) operation.
        • Yep. Squaring a number is an O(n^2) operation.

          Squaring a number with a naive algorithm is. With some decent algorithm it is O (n ln n). Like multiplying, division, square root, sine, cosine and many other functions.

          • There are a few very fast ways that work on only some numbers. Useful if you can be sure your inputs follow some constraints. This is why a lot of computer graphics either requires texture resolutions be a power of two, or performs faster if they are. You can multiply by powers of two just by using shift operations. Or divide, if you don't mind losing the remainder. Same idea as the 'just add a zero' rule to multiply by ten in decimal. Squareing an irrational number, though... there are no shortcuts for t
    • by 2.7182 (819680)
      A likely reason they may be computing pi^2 is because it is a pretty straightforward infinite series: pi^2 over 6 is the sum of 1 over n^2, n ranging from 1 to infinity.
      • I doubt it, though I do like that series. I can't quite remember generalizations of it, though.... That is, what is zeta(m) for m a positive integer? Wikipedia lists a formula valid at positive even integers here [wikipedia.org], wherein \zeta(2n) = \frac{(-1)^{n+1} B_{2n}(2 \pi)^{2n}}{2(2n)!}, so for instance 1 + 1/2^4 + 1/3^4 + ... = pi^4 / 90, and in general 1 + 1/2^(2n) + 1/3^(2n) + ... converges to r*pi^(2n) for some rational number r that can be found quite easily. I presume Euler's method (the one which first proved
    • What does that number "do"?

      Well, for one thing, you could use it to defeat computers in the future.

    • by BeanThere (28381)

      Pi is 'wrong' ... http://tauday.com/

    • by MoonBuggy (611105) on Saturday April 30, 2011 @08:26PM (#35987672) Journal

      Re:How many digists of pi do you know?

      ...one? [smbc-comics.com]

      • I used to know 36, but given that it's been some years since I memorised them I wouldn't trust my memory to be accurate any more. Typing and checking...
        3.14159265358979323846264338327950288.
        Yep. Still got them. But I can only recall by reciting them aloud.
    • by jamesh (87723)

      about 5 probably. My daughter can recite 50 or 100 or something like that.

      • by arth1 (260657)

        "50 or 100 or something like that"?
        That's like saying you have "1 or 2 cars or something like that" -- far too imprecise to be useful. In fact, 0 would satisfy "50 or 100 or something like that".

        • by dbc (135354)

          Ha ha.... while true, I sympathize with the grandparent. My daughter is also a Pi digit memorizer. She adds a few digits every so often, I can't keep track of how many she knows. I'd guess 75 or 100 or something like that. :) I don't think she knows or cares exactly how many digits of Pi she has memorized, as long as it is more digits than anyone else she meets...

    • by the_humeister (922869) on Saturday April 30, 2011 @10:31PM (#35988100)

      I know all of them. I just don't know which order they go in.

    • by rrohbeck (944847)

      OK I'm a dick.
      50.

    • by Abstrackt (609015) on Saturday April 30, 2011 @11:27PM (#35988308)
      "How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!" There you go, Pi to 14 digits in an easy to remember package. Count the letters in each word to get the right digits.
      • by arth1 (260657)

        "How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!" There you go, Pi to 14 digits in an easy to remember package. Count the letters in each word to get the right digits.

        Easily beaten by this common and far more memorable verse:

        How I wish I could enumerate Pi
        "Eureka!" cried the great inventor
        "Christmas pudding, Christmas pie
        is the problem's very center!"

        After hearing that one once, I could not help but remember pi to 20 decimals.

        If I want to be more precise, arccos(-1) will do.

        • Sir, I bear a rhyme excelling
          In mystic force and magic spelling
          Celestial sprites elucidate
          All my own striving can't relate
          Or locate they who can cogitate
          And so finally terminate.
          Finis.

          I did it backwards: I memorised the digits of pi directly, and use them to check my recollection of the verse. That's also as far as you're going in simple letter-counts, as the next digit is a zero.
    • YTMND inspired a lot of people to learn more digits of Pi. "Pi" by Hard n Phirm [ytmnd.com] became a minor fad there [ytmnd.com].
  • Not a disclaimer ... (Score:2, Informative)

    by Anonymous Coward

    "Disclaimers: I attended graduate school at U.C. Berkeley. I am presently employed by a software company that sells an infrastructure product named PI.""

    That's *not* a DISCLAIMER. That's a DISCLOSURE.

  • ...neither TFA nor TFBlog tell you which it is. So...flip a coin.
  • ... enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton

    Why bother carrying out the computation to such precision when the error in your measurement of the radius (or diameter) would be so much bigger.

    • It sounds like you think that's a statement about the pi they've calculated here, where the words immediately preceeding your quote, found at the top of this page, are "pi to 40 digits". Any of us could comfortably calculate that on paper in a day, or half an hour with a 10-digit solar powered calculator. I fear you may be guilty of slashdot-itis - an impulse to try and prove yourself smart by demolishing a strawman built from the headline, or the summary if we're lucky. Sometimes, the fail is too epic not

    • by martas (1439879)
      That was clearly meant for illustrative purposes; the complete statement would have been "if you knew the precise radius of a circular object approximately the size of the Milky Way galaxy, then a value of Pi to 40 digits would be more than enough to compute its circumference to an error less than the size of a proton." It was left up to the reader to infer the precise meaning of the shortened statement. Apparently you failed to do so, either due to lack of ability, or because you had adversarial intentions
  • by jd (1658)

    Not square.

    • Not square.

      Besides, a square pi is more of a cobbler, don't you think?

    • by rossdee (243626)

      Back in the land where I was born we had 'meat pies'. They weren't square exactly, more like rectangular with rounded corners.
      (No Apple Computer (TM) had nothing to do with it.)

      I only ever bothered memorizing 10 digits of Pi since that was the number of digits calculators had (back in '74 - it was an HP35

      • by jd (1658)

        In Ye Olde Country, the strangest meat pie was the crescent-moon-shaped Cornish pastie.

  • by 1729 (581437)

    Wow, a BlueGene/P is being used to run something other than Linpack. That's gotta be a first.

    Disclaimer: I didn't attend graduate school at U.C. Berkeley, nor am I presently employed by a software company that sells an infrastructure product named PI. I have, however, wasted way too much time trying to get codes to build and run (slowly!) on BG/* platforms.

  • by Lulu of the Lotus-Ea (3441) <mertz@gnosis.cx> on Saturday April 30, 2011 @09:53PM (#35987992) Homepage

    It's plain easy to calculate the sixty-trillionth digit of Pi... as long as you don't care about the digits that come before it: http://www.sciencenews.org/sn_arc98/2_28_98/mathland.htm [sciencenews.org].

    • 20 computers a month for the trillionth, much less all 60... trillion. A month with 20 computers for one digit still doesn't seem that straight forward.

      • by godrik (1287354)

        GP point is that computing a particular digit of pi is easy, you can even compute it manually. So in particular the 60 trilionth digit is easy to know. Knowing the first 60 trilionth digit is a much harder task.

        • That may have been the GP's point, but it's not really correct. It takes O(n^2) time to compute the nth digit of pi using a modification of the BBP formula. The linked article actually alludes to this fact, though only obliquely, in a reference to exponentiation by squaring. You certainly couldn't compute that manually, as in, with a pencil and paper. All is not lost though; more than the quadrillionth binary digit has been computed (though it took a distributed computing project many months), which is *way
  • You humans and your base-10 arithmetic. I use base-pi arithmetic. So pi = 1, and pi squared = 1. Computed in a nanosecond. Of course, it makes other computations slightly more complex. For example, I have about 3.183095825842514 fingers, more or less...
    • You humans and your base-10 arithmetic. I use base-pi arithmetic. So pi = 1, and pi squared = 1. Computed in a nanosecond. Of course, it makes other computations slightly more complex. For example, I have about 3.183095825842514 fingers, more or less...

      You just took 10 and divided it by pi and wrote that down, all in base 10. Also, pi in base pi would be 10, not 1 (like 2 is 10 in binary), and pi^2 is 100.

      I'm not certain how other numbers in a non-integer base would be written down, but I think 10 in base pi would be 100.010221222... (pi^2 + pi^-2 + 2*pi^-4 + 2*pi^-5...) There may be multiple representations of the same number. For example, I think 10 could also be 30.121...

      • There definitely would be multiple representations of numbers, allowing infinite decimal places and arbitrary integer "digits". You could write pi as 10 or as 3.(stuff that never ends), which is presumably what you meant to type. You could perhaps limit your decimal places to some set of integers, but that seems pretty artificial. Though, perhaps {0, 1} would be sufficient.... Nope. Even 0.111111... would max out at 1/(1-(1/pi)) ~= 1.47 pi. However, 3 would seem to work from an analogous analysis.
      • by S-100 (1295224)
        Of course I had to simplify my example for your terrans to be able to understand it. But don't you wish you knew how many fingers I really have?
  • Give me 10 attempts and I guarantee I can guess this digit faster than the computer can compute it.
  • The suspense is killing me.

    Of course, this being slashdot, I didn't RTFA.

  • Question: Knowing the diameter of the observable universe, how many digits of Pi are needed to calculate the circumference of the observable universe, accurate to within 1 plank length?
    Answer: 62 digits. Here they are: 3.14159265358979323846264338327950288419716939937510582097494459

    Calculated this one myself.

  • by Torodung (31985) on Saturday April 30, 2011 @11:05PM (#35988230) Journal

    I think it would be tremendously funny to find out, at some suitably ridiculous decimal place, that all subsequent places are zero repeating. It would utterly break some people's heads to find out that the number is only "very, very particular," rather than "irrational."

    It is the one hope that holds my interest when I read about crunching these numbers.

    • Re: (Score:3, Informative)

      by Anonymous Coward
    • There is a sequence of several 9's [wikipedia.org] fairly early in the decimal expansion of pi though. People have joked about memorizing pi out to 770 digits so they can say "...999999 and so on."

      But seriously, the irrationality of arctan(1) (which equals tau/8 or pi/4) has been proven [wikipedia.org].

    • Such a result would cause math, physics, and philosophy to come crashing down on everyone's heads. Pi's transcendence (hence, irrationality) is a beautiful consequence of the Lindemann-Weierstrass theorem [wikipedia.org]. The proof of that theorem is, well, hideous, but the statement is incredibly elegant. It turns linear independence into algebraic independence, from which the transcendence of both pi and e may be very quickly deduced. I believe that there are continued fraction proofs of pi's irrationality that are relat
  • 'A value of Pi to 40 digits would be more than enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton.'

    I freaking love mathematicians. Everything has a proof when you can't actually prove it, coming or going.

  • What IS the sixty trillionth digit of Pi? That's what I'd like to know.

Premature optimization is the root of all evil. -- D.E. Knuth

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