Bargain Supercomputer?

Humanoido · 2013-07-01 02:02

Whip out your credit card for this bargain basement deal. At only $420,000.00, its the cheapest supercomputer. A regular supercomputer costs 1.3 billion dollars.

http://www.youtube.com/watch?v=hSVo4ejZ7rc

Heater. · 2013-07-01 02:41

Yes but, the world record for calculating the most digits of PI has been held by single PC boxes since 2009. Now standing at 10 trillion digits! http://www.numberworld.org/misc_runs/pi-10t/details.html

These stupid super computers cannot touch it.

Calculating 10 trillion digits of PI might be a nice little exercise to warm up the Big Brain don't you think?

Martin_H · 2013-07-01 06:15

His use of check points is a good idea for a calculation that takes a year. Back in 2007 I was solving a programming puzzle to find the 51st billionth digit of a number. The calculations would only take a day or so, but running a computer continuously at 100% CPU for this amount of time turns out to be tricky. One run failed after a few hours because there was enough dust on the heat sink to slowly accumulate heat. The next run failed with out of memory after running for a day because of a slow memory leak.

Heater. · 2013-07-01 06:26

Yes, but perhaps you were not expecting earthquakes as he has in his log!

LoopyByteloose · 2013-07-01 08:55

I just can't imagine what I would need pi to 10 trillion digits for.
It seems I have been going in circle for many years without the aid of a super computer.

If one could tell me when to buy and sell stocks, or which horse to bet on... that would be something.

And I just have to wonder if that pi to 10 trillion digits is binary digits or decimal or what? Who would ever look at a decimal number that is created with 10 trillion digits? In binary form you might feed it to another computer... but that would take awhile.

Martin_H · 2013-07-01 09:25

Loopy, another thing to consider is that we don't know if it is correct until someone else checks his calculations! For example William Shanks (1812-1882) worked for years to find the first 707 digits of pi. Unfortunately, he made a mistake after the 527th place and the following digits were all wrong. But it took a while for anyone else to check.

As to why? Some mathematicians are curious if there are any patterns to the digits. However, computing large numbers is really the challenge. You can't set the problem up in memory and do the math. You first need to build the capacity to manipulate large numbers. Often you can get away with this because at any point in time most digits of the calculation are zero. But even recording 10 trillion digits is a challenge. In my 51 billionth digit problem I didn't bother to keep the number, so I used a circular buffer a few hundred digits long and keep wrapping around. I broke the calculation into steps and only kept needed results. But even that was a challenge.

Humanoido · 2013-07-01 16:50

Heater. wrote: »

Yes but, the world record for calculating the most digits of PI has been held by single PC boxes since 2009. Now standing at 10 trillion digits! http://www.numberworld.org/misc_runs/pi-10t/details.html These stupid super computers cannot touch it. Calculating 10 trillion digits of PI might be a nice little exercise to warm up the Big Brain don't you think?

It's warm! I'm already running 2 air conditioners. I don't know why a supercomputer cannot calculate pi to lots of places. Here's a reference to pi squared to 60 trillion digits as calculated with a supercomputer. http://energy.gov/articles/supercomputers-crack-sixty-trillionth-binary-digit-pi-squared "Australian researchers have done the impossible -- they’ve found the sixty-trillionth binary digit of Pi-squared! The calculation would have taken a single computer processor unit (CPU) 1,500 years to calculate, but scientists from IBM and the University of Newcastle managed to complete this work in just a few months on IBM's "BlueGene/P" supercomputer, which is designed to run continuously at one quadrillion calculations per second."

Ironic you should mention this topic. I have nothing or little to show now, however, playing continues with some possibilities of a potential future product, the Spin Brain - a Big Brain with a handful of enhanced Propeller chips in parallel. It demonstrates basic principles by taking some exampling characteristics of a supercomputer, in particular the notion of larger multiples of relatively simple processors communicating over a common bus, each doing a portion of a task in parallel. Compared to a single chip computer, there's more time involved in programming the task and preparing it so it's properly divided up into parallel chunks allowing each processor to run full throttle in simultaneous calculating and then assembling the bits into a single result upon completion. The challenge is minimizing a speed compromise that happens when the calculation process is interrupted for a memory dump or output operation when dealing with very long strings of numbers.

Humanoido · 2013-07-01 17:08

There's lots of answers to "Why Pi?"

http://energy.gov/articles/supercomputers-crack-sixty-trillionth-binary-digit-pi-squared

"For example in 1986, a Pi-calculating program that Bailey wrote at NASA, using an algorithm due to Jonathan and Peter Borwein, detected some hardware problems in one of the original Cray-2 supercomputers that had escaped the manufacturer’s tests. Along this same line, some improved techniques for computing what is known as the fast Fourier transform on modern computer systems had their roots in efforts to accelerate computations of Pi. These improved techniques are now very widely employed in scientific and engineering applications. And of course, from a mathematical perspective it’s just plain fascinating to see the digits of Pi in action!"

Heater. · 2013-07-03 05:20

@Martin_H,

Loopy, another thing to consider is that we don't know if it is correct until someone else checks his calculations!

Of course we need third party verification for any world record claim. Remarkably it turns out that having spent a long time calculating the 10 trillion digits you can check the accuracy of your result very quickly. There are algorithms for calculating the Nth digit of Pi. You don't get all the digits up to N, just the Nth one. See Plouffe's Formula and Bellard's Formula. They are interesting looking objects.

So:
1) Calculate your 10 trillion digits using the formula from the Chudnovski brothers. This spectacular looking formula gives you just over 14 digits of accuracy per iteration.
2) You will have been working in binary so convert that to decimal.
3) Calculate a bunch of least significant digits using Plouffe and Bellard formulae.
4) If those last digits cross check OK then you are done.

See here for the formula and explaination of how the checking works:
http://www.numberworld.org/misc_runs/pi-5t/details.html#formulas

@Humanoido,

I don't know why a supercomputer cannot calculate pi to lots of places.

I'm sure they can but the fact is that super computers have not held the record since 2009. This was a big surprise to me. Had you asked me a month ago i would have assumed that calculating 10 trillion digits of Pi would take so long that a super computer was essential. Turns out that the most effective algorithm known for calculating digits of Pi is the Chudnovski formula. That formula turns out to be very hard to parallelize. You rapidly run into a huge communications bottleneck. Even on a super computer it will take a long time and is probably too expensive to think about. Also when working with huge numbers like this you are probably not using floating point units but working with arrays of integers. All those GPU's that are in vogue now do not help.

@Humanoid

Here's a reference to pi squared to 60 trillion digits as calculated with a supercomputer....

It did not calculate 60 trillion digits of Pi. It calculated only the 60 trillionth digit. Not the preceding digits. See above. (Edit: Not even that. It was " sixty-trillionth binary digit of Pi-squared" as you quoted yourself. So actually they only produced one bit for their effort!)

@Loopy Byteloose

And I just have to wonder if that pi to 10 trillion digits is binary digits or decimal or what? Who would ever look at a decimal number that is created with 10 trillion digits?

Turns out the calculation is done in binary and turned to decimal when done. That conversion took 18 days! See links above for the procedure.

In binary form you might feed it to another computer... but that would take awhile.

Yeah. It's just a ten terabyte file at the end of the day. Presumably you can copy it to some other machine faster than recalculating it on that other machine:)

Humanoido · 2013-07-03 23:08

Heater wrote: It did not calculate 60 trillion digits of Pi. It calculated only the 60 trillionth digit. Not the preceding digits. See above. (Edit: Not even that. It was " sixty-trillionth binary digit of Pi-squared" as you quoted yourself. So actually they only produced one bit for their effort!)

Some time ago, I had looked at developing an algorithm to calculate pi to higher digits on a parallel supercomputer. It's not in front of me now, but I wanted to assign chunks of the formula to each paralleled processor to calculate a specific digit, output, then shift the sequence and continue. It seemed to suit parallel structures just fine. I'm not sure if this is practical or not, but would like to pick it up again in the future and see where it leads.

Bargain Supercomputer?

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