New Pi Computation Record Using a Desktop PC

Verification by Tukz · 2010-01-04 19:38 · Score: 3, Interesting

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. -

Re:Verification by msclrhd · 2010-01-04 20:15 · Score: 3, Informative

In TFA (especially the PDF), the verification method is to use another algorithm to check the output. The PDF on Fabrice's home page goes into more details.
NOTE: The machine they were using to generate the second result broke, so they used another (3rd) algorithm to generate the last digits.
Re:Verification by David+Jao · 2010-01-04 20:20 · Score: 4, Interesting

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.
Perhaps this is why you should read the article. The press release answers this question directly.

The binary result was verified with a formula found by the author with the Bailey-Borwein-Plouffe algorithm which directly gives the n'th hexadecimal digits of Pi. With this algorithm, the last 50 hexadecimal digits of the binary result were checked. A checksum modulo a 64 bit prime number done in the last multiplication of the Chudnovsky formula evaluation ensured a negligible probability of error.
The conversion from binary to base 10 was verified with a checksum modulo a 64 bit prime number.
Re:Verification by Xest · 2010-01-04 20:34 · Score: 1

You don't need to verify that the number is correctly pi to the given digits, merely verify that the algorithm calculates the digits of pi correctly.
The algorithm can be proven correct in a number of relatively quick and easy ways.
The algorithm is really also arguably the most important part anyway rather than the digits themselves because it's the part of most use.
Re:Verification by KowShak · 2010-01-04 21:06 · Score: 1

The mathematical algorithm may be correct, but is the implementation of it correct and how do you verify it?
A computer program can not be proven to be correct in a number of relatively quick and easy ways.
Re:Verification by SlothDead · 2010-01-04 22:01 · Score: 1

That does not really matter at all. It's not about getting a lot of correct digits of Pi.
Re:Verification by Xest · 2010-01-04 22:21 · Score: 1

No, because most software is large and complex, doing things like mathematical induction on all code is infeasible for this reason.
In contrast, code to calculate something like this is relatively extremely small.
Effectively, the reason your argument doesn't hold is that although we can fairly trivially prove some algorithms correct, the method isn't scalable and hence doesn't scale to the scale of pretty much any piece of modern software.
Re:Verification by dch24 · 2010-01-04 22:37 · Score: 1

Breaking the record brings attention to the algorithm.

It means that the algorithm will get noticed.
Re:Verification by Xest · 2010-01-04 22:54 · Score: 2, Interesting

The implementation (compiled or uncompiled) is in itself an algorithm which can equally be checked because the language follows pre-defined logical rules which may act as axioms or depending on the details of the algorithm it may be trivial to just use induction.
It's not like we're checking a full operating system or office suite here, so size isn't a restrictive problem in such a proof.
It may be that the processor itself hasn't been checked so that the results of executing that algorithm isn't correct either, but again, when it's the algorithm that matters, who cares? We know the specifications of the language which may effectively act as axioms in a proof. The compiler may not be valid certainly, but as long as the algorithm (yes, mathematical and implementation) is correct then that is what matters.
It is down to anyone then using the algorithm to ensure the other layers are correct enough for their purposes.
Re:Verification by Anonymous Coward · 2010-01-05 00:08 · Score: 1, Insightful

But the fact that the algorithm runs is the best proof of it working.
And it is also an exercise in practicality; the author notes in the PDF that there was a high probability of a random bit error during the 100+ day computation period. It is in a way important to show that yes, long computations can be done and verified on ordinary hardware without ECC.
Re:Verification by ChienAndalu · 2010-01-05 01:00 · Score: 1

From the PDF on his website:

A standard desktop PC was used, using a Core i7 CPU at 2.93 GHz. This CPU
contains 4 physical cores.
We put only 6 GiB of RAM to reduce the cost. It means the amount of RAM
is about 170 times smaller than the size of the final result, so the I/O performance
of the mass storage is critical. Unfortunately, the RAM had no ECC (Error
Correcting Code), so random bit errors could not be corrected nor detected. Since
the computation lasted more than 100 days, such errors were likely [12]. Hopefully,
the computations included verification steps which could detect such errors.
For the mass storage, five 1.5 TB hard disks were used. The aggregated peak
I/O speed is about 500 MB/s.
A weird choice of words...
Re:Verification by Terje+Mathisen · 2010-01-05 01:02 · Score: 2, Interesting

Verification as actually quite easy, due to the (totally unexpected at the time!) discovery of the Borwein-Bailey-Plouffe algorithm which allows you to directly calculate the N'th hexadecimal digit of pi, without having to determine any other digits.
He used this on a bunch of the last digits and they all came out correct, which makes the probability of an error extremely small.
Last year I used his algorithm to calculate 1e9 (i.e. a US billion) digits of pi and made them searchable:
http://tmsw.no/pi-search/
Try to enter any string of digits, like a full 8-digit birth day: The odds are good that pi-search will locate it somewhere.
Terje
PS. Yes, I did use his table just now to verify that my own digits are correct. :-)

--
"almost all programming can be viewed as an exercise in caching"
Re:Verification by Stooshie · 2010-01-05 02:36 · Score: 1

"But the fact that the algorithm runs is the best proof of it working"

Eh?

I, and all other programmers, have written plenty algorithms that run. That does not mean it works correctly according to the initial spec.

--
America, Home of the Brave. ... .and the Squaw.
Re:Verification by rafaelolg · 2010-01-05 03:14 · Score: 1

I guess if one proves that the program is formally proof correct there is no need to verify the numbers.
Re:Verification by noidentity · 2010-01-05 04:05 · Score: 1

Fascinating about the Bailey-Borwein-Plouffe formula for quickly generating an arbitrary digit of pi. Reading the FAQ, he doesn't offer the entire series of PI, but does offer excerpts. The devil's advocate in me can't help but point out that he could have prepared these excerpts using the above formula, rather than actually calculating pi to that many places. I suppose even if he did offer the entire result, nobody could verify it except by generating it himself.
Re:Verification by RockDoctor · 2010-01-05 15:41 · Score: 1

Last year I used his algorithm to calculate 1e9 (i.e. a US billion) digits of pi and made them searchable:
Makes me hanker (a little) for my past days in PiHex.
101,112,412 is an interesting location.

--
Birds are not dinosaur descendants;birds are dinosaurs, for all useful meanings of "birds", "are" and "dinosaurs"
Re:Verification by Terje+Mathisen · 2010-01-05 19:10 · Score: 1

101,112,412 is an interesting location.
Interesting...
Were you born on July 12th 1965 or is there something else I didn't notice?
Terje

--
"almost all programming can be viewed as an exercise in caching"
Re:Verification by koollman · 2010-01-08 04:20 · Score: 1

Unless you assume the program is then run on real hardware, with possibilities of failure and unexpected behaviors.
Formal proof verifies that it corresponds to the specifications, which means it won't be the algorithm's fault if the result is wrong. It leaves many other possibilities for failure (including problem in the specification proved, or hardware troubles).
Re:Verification by RockDoctor · 2010-01-08 16:50 · Score: 1

Were you born on PI(101,112,412)or is there something else I didn't notice
You got it. I'm now wondering who has that phone number (and in which countries.)?

--
Birds are not dinosaur descendants;birds are dinosaurs, for all useful meanings of "birds", "are" and "dinosaurs"

Poster must work in banking by dredwerker · 2010-01-04 19:38 · Score: 1

if they think 1.2 billion is small

--
On a long enough timeline. The survival rate for everyone drops to zero. Chuck Palahniuk, Fight Club, 1996

Thats nice and all... by fliptw · 2010-01-04 19:39 · Score: 2, Funny

But will it help us in getting flying cars?

Re:Thats nice and all... by LostCluster · 2010-01-04 19:48 · Score: 5, Funny

Only if you avoid the square routes.
Re:Thats nice and all... by mcgrew · 2010-01-05 02:37 · Score: 1

What's the square route of pie?
Cherries!

--
Free Martian Whores!
Re:Thats nice and all... by HTH+NE1 · 2010-01-05 07:12 · Score: 1

The Doctor: Why are you repeating?
Sky Silvestry: Why are you repeating?
The Doctor: What is that, learning?
Sky Silvestry: What is that, learning?
The Doctor: Copying?
Sky Silvestry: Copying?
The Doctor: Absorbing?
Sky Silvestry: Absorbing?
The Doctor: The square root of pi is 1.7...
Sky Silvestry: [talking over] The square root of pi is...
The Doctor: 7245385090...
Sky Silvestry: 1.77245385...
The Doctor: 551602729...
Sky Silvestry: 090551602...
The Doctor: 816748334...
Sky Silvestry: 729816748...
The Doctor: 1. Wow.
Sky Silvestry: 3341. Wow.

--
Oh, say does that Star-Spangled Banner entwine / The myrtle of Venus with Bacchus's vine?

One thing to say by DirtyCanuck · 2010-01-04 19:42 · Score: 5, Informative

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.

Re:One thing to say by Anonymous Coward · 2010-01-04 20:15 · Score: 1, Insightful

Interesting, but it didn't really answer the question.
Re:One thing to say by Anonymous Coward · 2010-01-04 20:19 · Score: 4, Funny

HE USED TRICKS!!!!1111Burn the witch...eehh communist...eeeh climate researcher...eeeeh....PI guy.
Re:One thing to say by PingPongBoy · 2010-01-04 20:20 · Score: 1

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.
Before the next Top 500 list is published in June, maybe the benchmarking needs to be shaken up a little, huh? Intuition suggests the supercomputer could be reprogrammed to calculate more digits by a few orders of magnitude. We still have a lot to learn when it comes to taken advantage of multiprocessors, as well as algorithms.

--
Know your pads. One time pad: good for cryptography. Two timing pad: where to take your mistress.
Re:One thing to say by PinkyGigglebrain · 2010-01-04 20:24 · Score: 4, Interesting

An answer is a reply but a reply is not always an answer.
Re:One thing to say by digitalhermit · 2010-01-04 21:04 · Score: 4, Insightful

In another thread someone had posted that there was no reason for any modern CPUs; the idea being that anything one could reasonably want to do with a computer was possible with decade old hardware.
This.. *This* article is why I enjoy the breakneck pace of processor speed improvements. The thought of being able to do some pretty serious computing on a relatively inexpensive bit of hardware -- even if it takes half a year to get results -- does what the printing press did. 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. Sure, all that you need to do some serious mathematics is a pen and paper, but more and more discoveries occur using methods that can only be performed with a computer.
There's always the argument that cheap computers and cheap access to powerful software pollutes the space with hacks and dilletantes. People have said this about desktop publishing, ray tracing, and even the growth of Linux. But it's this ability to do some amazing things with computers that makes it all worthwhile.
Re:One thing to say by HateBreeder · 2010-01-04 21:22 · Score: 3, Interesting

I would assume he only needs to verify the last 120 billion digits.
Assuming his algorithm can support serialization of its state into a check-point, he can simply recalculate the last 120 billion digits a couple of times and compare.
Assuming linear time to compute each digit: 120e9/2.7e12 * 116 =~ 5 days. not too bad.

--
Sigs are for the weak.
Re:One thing to say by Ego_and_his_own · 2010-01-04 22:09 · Score: 1

There is something in Pi that is far beyond numbers. It hides an answer to some questions for sure. It puts math on abstract side of reality. Pi is weird....
Re:One thing to say by dch24 · 2010-01-04 22:36 · Score: 1

Come on... think a little.

What does large number theory, factorization, optimizations that offer 2000x speedups in this field, and specific information for desktop computers ... what is it about?

Go watch Sneakers again.
Re:One thing to say by Le+Marteau · 2010-01-04 22:53 · Score: 3, Funny

> It hides an answer to some questions for sure.
Could be. I'm not sure the answer will be in base 10, though.
Maybe, in base 36, beginning at the trillionth digit, pi is:
"URTEHSUXXORUNEED2GETALIFESRSLYKTHXBYE"
That would be amazing.

--
Mod down people who tell people how to mod in their sigs
Re:One thing to say by Lord+Lode · 2010-01-04 23:01 · Score: 2, Interesting

Hmm, for such a record attempt, do you actually have to calculate all these earlier digits? They're already known. Can anyone prove the computer calculated the already known digits first (instead of getting them from a table) before finally getting to the 120 million new ones?
Re:One thing to say by Le+Marteau · 2010-01-04 23:03 · Score: 1

Seriously, though... rather than going off into trying to pushing the limit on how many digits can be cranked out for pi, would it not be more interesting and perhaps more fruitful to search for patterns, in numerous bases, in pi? Maybe there really IS "an ultimate answer" in some other base, just waiting for some geek in his mother's basement with an old Packard Bell to invest the energy.
Or maybe pi will end up just being a bunch of zeros or something after X many digits.
Either way, I'm sure it would make the front page of /.

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Mod down people who tell people how to mod in their sigs
Re:One thing to say by MrMr · 2010-01-04 23:04 · Score: 1

Worse than that, I find it extremely unlikely that not a single bit failed in uncorrected memory during the whole 116 days...
see for instance:here
Re:One thing to say by Anonymous Coward · 2010-01-04 23:37 · Score: 1, Interesting

In 1960 or so the tree-ring data, which before was quite good at correlating with climate data, started to diverge, likely due to acid rain and other air pollution. So it was a known fact that tree ring data past that time was no good at giving climate information, so they replaced it with data that was known to give accurate climate data. Thats all what the "hide the decline" was about.
Or to put it another way: The pollution is already so bad that the data collection gets screwed up and that is now used as an argument that nothing is wrong. Way to go logic...
Re:One thing to say by paiute · 2010-01-05 00:33 · Score: 1

If the expression of pi in any base is random, eventually any message you want will be found within it. You do not need 1000K monkeys to output all of some dead guy's work, which is good, because that would be a lot of monkey doo you would have to clean up waiting for them to finish. And you would have copyright problems to boot.

--
If Slashdot were chemistry it would look like this:Cadaverine
Re:One thing to say by dtmos · 2010-01-05 00:36 · Score: 2, Funny

Of course, the first step in your plan is to calculate the digits in the first place...
Re:One thing to say by Muad'Dave · 2010-01-05 00:47 · Score: 1

You mean like a base-11 raster of 1's and 0's that forms a perfect circle ?

--
Tiller's Rule: Never use a word in written form that you've only heard and never read. You will end up looking foolish.
Re:One thing to say by arth1 · 2010-01-05 01:14 · Score: 1

Come on... think a little.
What does large number theory, factorization, optimizations that offer 2000x speedups in this field, and specific information for desktop computers ... what is it about?
Psychologically, it's rather obvious that it's peacocking.
That said, it may have some positive side effects down the road, if nothing else for making more people understand that tailoring solutions around bottlenecks can often give better results than raw power.
Re:One thing to say by ceoyoyo · 2010-01-05 01:40 · Score: 1

Give that someone a decade old processor and see how happy he is.
Re:One thing to say by gbutler69 · 2010-01-05 01:48 · Score: 1

Isn't there a proof that PI is irrational? If so, then, no it will never repeat.

--
Over-the-top Response Guy! Giving "Over-the-Top Responses" since 1970.
Re:One thing to say by JackDW · 2010-01-05 01:49 · Score: 1

Like a Mandelbrot fractal, or the number e, Pi has the interesting property that it's full of detail, but derived from a simple rule. So yes, it is interesting.
What I find most interesting about such things is their universality. If one was to suggest the existence of some God, then go on to say that this God created the universe where we live, one could still never claim that Pi had been created or assigned a value at that time. No, Pi was never created, it simply is, and it is everywhere always the same. A universe with a different value of Pi would be impossible.
Ironically, the "thumbprint of God" is exactly what these things are not.

--
You're an immobile computer, remember?
Re:One thing to say by rwa2 · 2010-01-05 02:39 · Score: 1

I used to think that, but you'd need some kind of weird compression / decompression. You can't find absolutely *any* pattern in irrational numbers... no repeating digits or zeros.
Re:One thing to say by axis_omega · 2010-01-05 02:59 · Score: 1

What's wrong with /. today ? mod the guy funny duh. Let me see, he is obviously not a troll. Informative ? a little yeah.
Can I have sarcasm mod point then ?
I have a question and didn't bother to search it yet. But I know that PI is related to "e" somehow. Can we do the same with the digits of "e"
and if so, how come PI is more popular ?
Shouldn't we consider "e" a little bit more ?

--
It's funny how I make sense to others and not myself...
Re:One thing to say by apterium · 2010-01-05 03:16 · Score: 1

For such a computation, generally the precision of the result depends on the precision of some intermediate values (which themselves depends on the algorithm). If you only have access to actually known decimals computed by someone else, you have to redo the whole computation from the beginning.
Re:One thing to say by Hognoxious · 2010-01-05 03:28 · Score: 1

What if I answer with a question?

--
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Re:One thing to say by electrosoccertux · 2010-01-05 04:11 · Score: 1

If you reply to the first post, it's almost just as good as having the 1st post. You get more views. So then the next guy replies to that reply, so on and so forth. Mods be on the lookout for offtopic.
Re:One thing to say by onepoint · 2010-01-05 04:15 · Score: 1

I would love to give you mod points as insightful.
The first thing I thought of after reading was .... How to run this as a 10 minute test on a personal computer as a benchmark I/O.
I looked at the FAQ and it seemed that ram was not the real issue but the I/O is the most important part. so again, this might be the best tool for testing systems for I/O performance ...
I would think that it might be interesting to test this on raid systems, database servers and anything that has a ton of read/writes and since it might not be cheat-able it could be something that a specific segment of the industry might want.
I just thought of this, this tool could be used to test network performance of routers ( have a drive siting on another address on the network, and run the data back and forth ) ...

--
if you see me, smile and say hello.
Re:One thing to say by stephentyrone · 2010-01-05 04:16 · Score: 2, Insightful

Pi is interesting in that regard -- there are algorithms that can compute the Nth digit without needing to compute the intermediate digits. If you want to compute all digits from 0 to N, however, there are more efficient algorithms.
Re:One thing to say by kill-1 · 2010-01-05 04:16 · Score: 1

pi isn't random in any base. In base pi it's 10.
Re:One thing to say by onepoint · 2010-01-05 04:19 · Score: 1

not to troll, but what would it take to have a universe that Pi would equal a rational number?

--
if you see me, smile and say hello.
Re:One thing to say by CrimsonAvenger · 2010-01-05 04:33 · Score: 1

No, Pi was never created, it simply is, and it is everywhere always the same. A universe with a different value of Pi would be impossible.

Last I checked, the value of Pi we use is the one for Euclidean geometry. For non-Euclidean geometry, pi has different values, depending on the curvature of the surface that is the basis for the geometry.
Note, by the by, that we don't actually live in a Euclidean geometry, but that the curvature is small enough that the ideal euclidean value of pi still works.

--

"I do not agree with what you say, but I will defend to the death your right to say it"
Re:One thing to say by HTH+NE1 · 2010-01-05 04:55 · Score: 1

Maybe, in base 36, beginning at the trillionth digit, pi is:
"URTEHSUXXORUNEED2GETALIFESRSLYKTHXBYE"
That would be amazing.
Well, take that base36 string, convert it into a base10 string, and search for it.

--
Oh, say does that Star-Spangled Banner entwine / The myrtle of Venus with Bacchus's vine?
Re:One thing to say by Hatta · 2010-01-05 06:05 · Score: 1

In another thread someone had posted that there was no reason for any modern CPUs; the idea being that anything one could reasonably want to do with a computer was possible with decade old hardware.
This.. *This* article is why I enjoy the breakneck pace of processor speed improvements.
But this is pretty pointless. What value is there in knowing the 2.7 trillionth digit of pi? I appreciate advances in processor technology because they speed up encryption, encoding, and rendering, but not this. Those cycles would have been put to better use participating in folding@home or some such.

--
Give me Classic Slashdot or give me death!
Re:One thing to say by CecilPL · 2010-01-05 06:15 · Score: 1

Sure you can - at least any given finitely long string of repeating digits. There is a repeating string of 6 "9"s in pi between digits 762 and 767.
Re:One thing to say by John+Hasler · 2010-01-05 14:43 · Score: 1

I have a question and didn't bother to search it yet. But I know that PI is related to "e" somehow.
Euler's identity: e^(i*pi) + 1 = 0. Also see e: Known Digits .

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Warning: this article may contain humor, sarcasm, parody, and perhaps even irony. Read at your own risk.
Re:One thing to say by st0nes · 2010-01-05 19:46 · Score: 1

not to troll, but what would it take to have a universe that Pi would equal a rational number?
One with non-circular circles.

--
Tempora mutantur, nos et mutamur in illis
Re:One thing to say by rwa2 · 2010-01-06 03:27 · Score: 1

Wow, cool, thanks for introducing me to the Feynman point... I guess I can resume my search for meaning in irrational digits now :>
Re:One thing to say by the_enigma_1983 · 2010-01-06 18:40 · Score: 1

Running folding@home just grinds the same algorithms over and over. From TFA

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.
So he's found a difference in algorithm efficiency based on computer architecture, and also improved the algorithm.
You might think his results may be lesser than what folding@home gets, but I think his methods are more valuable, when compared against what would've been learnt by letting the computer run folding@home.

Finally! by pEBDr · 2010-01-04 19:45 · Score: 5, Funny

Now I can finally get somewhat reasonable precision when calculating the radius of stuff!

Re:Finally! by Opportunist · 2010-01-04 19:54 · Score: 1

It's still waaaaaaaay off.
Can't get precision anymore these days, everything's just rush-rush, nobody takes the time to do it right...

--
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
Re:Finally! by WillyDavidK · 2010-01-04 20:23 · Score: 1

Too bad you'll need to upgrade your TI-83 to about 1.2TB of storage space to manipulate the number! And I hope you have some AAs that can last a few years under load...

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For lack of a better signature...
Re:Finally! by asc99c · 2010-01-04 21:15 · Score: 2, Funny

You'd also need something to prop up the other end of the new extended screen to display the number - Venus should be in about the right place when it gets a bit closer!
Re:Finally! by Anonymous Coward · 2010-01-04 21:57 · Score: 2, Interesting

There is a program package for Linux called Sage math where you can get a lot of digits in your constants. For example, to accurately calculate the circumference of a circular table with diameter=1000 mm you could type:
1000*pi().n(digits=1000000)
All you need now is a decent measuring tape...
These two also work, in case you're worried about not getting good enough accuracy when you calculate Fourier coefficients or something:
(pi().n(digits=1000000))^2
(pi().n(digits=1000000))^3
Since Sage sets up a web server on your computer you can even do this inside a decent phone web browser, so you can get that precision out in the field, where you need it. :-)
Re:Finally! by Anonymous Coward · 2010-01-04 23:03 · Score: 1, Funny

I still use the "old math", where you "measure" the radius. Now you kids calculate the radius with pi?
BTW, get off my lawn ...
Re:Finally! by HTH+NE1 · 2010-01-05 06:59 · Score: 2, Insightful

I think you'll find you don't need anywhere near that level of precision of pi to find the radius of the Universe in Planck lengths. 50 digits is sufficient.

--
Oh, say does that Star-Spangled Banner entwine / The myrtle of Venus with Bacchus's vine?
Re:Finally! by FrameRotBlues · 2010-01-05 11:30 · Score: 1

That's really the question I have: What's the point of such accuracy? Anything beyond 50 or a hundred digits past the decimal point is seemingly academic to me. Will anyone actually do a calculation using pi as a variable with a 2.7 billion digit accuracy?

Wow... by LostCluster · 2010-01-04 19:46 · Score: 1

They figured this out... they post some, not all of the data, and therefore survive the slashdotting.

Re:Wow... by MichaelSmith · 2010-01-04 19:50 · Score: 3, Interesting

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
Re:Wow... by kae_verens · 2010-01-04 20:58 · Score: 1

lol! nice. and for those that don't get it, read Contact by Carl Sagan.
Re:Wow... by Anonymous Coward · 2010-01-04 21:05 · Score: 1, Funny

Plain html is a wonderful thing.
yes, but why not do it in javascript? generating those digits on the fly is much more efficient from a slashdotting perspective.
Re:Wow... by CraterGlass · 2010-01-04 22:25 · Score: 1

Someone should check it for ASCII codes. Somewhere in there it probably says "Help! I'm being held prisoner in a universe factory!". (kudos to XKCD)
Re:Wow... by MichaelSmith · 2010-01-04 22:54 · Score: 1

Though I don't know what we would do with such a message. Might be a bit late to help.

--
http://michaelsmith.id.au
Re:Wow... by HeckRuler · 2010-01-05 04:21 · Score: 1

Well, since pi is an irrational number it has an infinite amount of decimal places which would convert into an infinite number of characters. Presumably with a random distribution. Chaos theory tells us that given an infinite supply of chaotic events, no matter the odds, every combination WILL occur.

So there is no "probably", somewhere in the digits of pi it does read "Help! I'm being held prisoner in a universe factory!".

this guy has a pretty impressive track record by Trepidity · 2010-01-04 19:47 · Score: 5, Informative

For those not previously familiar with Fabrice Bellard, he's known for:

LZEXE, very popular in the early 1990s as the first EXE-shrinker for DOS, or at least the first widely available one
ffmpeg, video decoding library which he started and headed for a number of years
QEMU, dynamic-translating generic emulator

--
10 PRINT CHR$(205.5+RND(1)); : GOTO 10

Re:this guy has a pretty impressive track record by msclrhd · 2010-01-04 20:28 · Score: 5, Informative

He also wrote the Obfuscated Tiny C Compiler (http://bellard.org/otcc/) in 2002 for the Obfuscated C contest, where otcc could compile itself. This became the Tiny C Compiler (TCC) which was picked up by Robert Landley (but subsequently dropped a while later) that is a capable, fast C90/C99 compiler.
His projects page (http://bellard.org/) and the older projects (http://bellard.org/projects.html) contain a lot of interesting projects.
Also of note: Fabrice achieved the record for Pi computation in 1997 as well:
http://bellard.org/pi/pi_hexa.html
http://bellard.org/pi-challenge/announce220997.html
http://bellard.org/pi/
Re:this guy has a pretty impressive track record by Rapha222 · 2010-01-04 23:39 · Score: 2, Insightful

Does this guy is God ?

Specs from the PC in question by c0mpliant · 2010-01-04 19:52 · Score: 4, Informative

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

Re:Specs from the PC in question by l0b0 · 2010-01-04 22:00 · Score: 2, Informative

He will be releasing the program he created for Windows (64bit only) and Linux
PS: Not the source

He needs some help... by LostCluster · 2010-01-04 19:54 · Score: 5, Funny

1 TB data files... somebody needs to help him with the compression! Oh, wait a minute.

Re:He needs some help... by phantomfive · 2010-01-04 20:56 · Score: 1

Wait, I have it right here! (could have gotten it inline, but slashdot doesn't do unicode, sorry).

--
Qxe4
Re:He needs some help... by russotto · 2010-01-05 02:47 · Score: 1

1 TB data files... somebody needs to help him with the compression!

Here's a full-precision compressed representation of Pi. The trick, of course, is expanding it:
pi = 4 * sum(k,0,+inf, ((-1)^k)/(2k+1)))

silly by dsanfte · 2010-01-04 20:00 · Score: 1, Flamebait

There is an algorithm now for calculating the nth digit of Pi at a whim.

This is slightly retarded.

--
occultae nullus est respectus musicae - originally a Greek proverb

Re:silly by Trepidity · 2010-01-04 20:04 · Score: 5, Informative

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:

I am not especially interested in the digits of Pi, but in the various algorithms involved to do arbitrary-precision arithmetic. Optimizing these algorithms to get good performance is a difficult programming challenge.
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
Re:silly by David+Jao · 2010-01-04 20:18 · Score: 3, Insightful

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.
Re:silly by i.of.the.storm · 2010-01-04 20:32 · Score: 1

Yeah, it's more interesting how he exploited caching to good effect with his algorithm. This is not something we hear about all that often.

--
All your base are belong to Wii.
Re:silly by Bacon+Bits · 2010-01-04 21:19 · Score: 2, Interesting

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.
Re:silly by Ambiguous+Puzuma · 2010-01-04 21:28 · Score: 4, Informative

There is no known formula or algorithm for calculating the n-th decimal digit directly.
What about this?

I present here a way of computing the nth decimal digit of pi (or any other base) by using more time than the [BBP] algorithm but still with very little memory.
Re:silly by Tim+C · 2010-01-04 21:47 · Score: 1

That's like saying that the fact that we have horses and cars, etc, make hiking or cycling anywhere retarded.
Sometimes the point isn't the destination, it's the journey.

--
It's official. Most of you are morons.
Re:silly by AlecC · 2010-01-04 22:39 · Score: 1

And he used that algorithm to verify his result by checking the last 50 digits.But, presumably, the algorithm he used for calculating the whole block is faster than this arbitrary algorithm, so it would not have generated his billions of digits in the time he has actually taken. The achievement is to calculate all those digits on relatively low powered hardware, not any particular bits.

--
Consciousness is an illusion caused by an excess of self consciousness.
Re:silly by AlecC · 2010-01-04 22:42 · Score: 1

But pi seems to have to do with more than geometry. It seems to be embedded in the structure of space and particle physics in some way we do not really understand. That said, of course we will never be able to make measurements whose total range is more than a few tens of orders of magnitude, so for physics, a short approximation is adequate. But mathematics exists in its own right - the fact that it serves physics has always been secondary (to mathematicians).

--
Consciousness is an illusion caused by an excess of self consciousness.
Re:silly by krou · 2010-01-04 23:02 · Score: 1

I thought it was 42 digits?

--
'If Christ had tweeted the sermon on the mount, it might have lasted until nightfall.' - John Perry Barlow
Re:silly by Whiteox · 2010-01-04 23:10 · Score: 1

Knowing Pi to 40 or so places

Face it, we all should know by now it's 42

--
Don't be apathetic. Procrastinate!
Re:silly by Stooshie · 2010-01-05 03:23 · Score: 1

That is a great engineering answer. Technically correct and calculated all the factors brilliantly.

However Pi is not just used for measuring physical objects.

An engineer, a physicist, and a mathematician were on a train heading north, and had just crossed the border into Scotland.

The engineer looked out of the window and said "Look! Scottish sheep are black!"
The physicist said, "No, no. Some Scottish sheep are black."
The mathematician looked irritated. "There is at least one field, containing at least one sheep, of which at least one side is black."

--
America, Home of the Brave. ... .and the Squaw.
Re:silly by ericcantona · 2010-01-05 03:55 · Score: 1

thanks for posting this. what a beautiful relation. it is occasionally coming across nuggets of gold like this that keeps me reading slashdot (although, to continue the analogy, it must be said that there is a whole lot of prospecting through cr*p required!).

--
When the seagulls follow the trawler, it's because they think sardines will be thrown in to the sea
Re:silly by David+Jao · 2010-01-05 04:58 · Score: 2, Informative

There is no known formula or algorithm for calculating the n-th decimal digit directly.
What about this?

I present here a way of computing the nth decimal digit of pi (or any other base) by using more time than the [BBP] algorithm but still with very little memory.
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.
Re:silly by sproingie · 2010-01-05 06:09 · Score: 2, Interesting

Angstroms are awful big. Just for the sake of maximum precision, how many digits would you need if you were measuring in planck lengths?
Re:silly by TenDimensions · 2010-01-05 06:23 · Score: 1

So I guess he's not just dividing 22 by 7?
Re:silly by Lost+Race · 2010-01-05 08:07 · Score: 1

"almost all programming can be viewed as an exercise in caching" --Terje Mathisen (another HPC god)
Re:silly by ChrisMaple · 2010-01-05 17:34 · Score: 1

More than 130 digits are needed to calculate the the number of electrons that would fill the universe.

--
Contribute to civilization: ari.aynrand.org/donate

Re:So... umm... by MichaelSmith · 2010-01-04 20:06 · Score: 3, Insightful

Could someone fill me in what purpose that may be?

Because.

--
http://michaelsmith.id.au

Re:So... umm... by Trepidity · 2010-01-04 20:08 · Score: 3, Informative

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

Did he find a message? by wisebabo · 2010-01-04 20:17 · Score: 1

I believe in "Contact" (the book by Carl Sagan, not the movie), the travelers ask the superintelligent aliens "Do you believe in God? To which they reply: "Yes" When asked why, they say "We have proof" in the finding of a message in a transcendental number (pi?).

After reading the Wikipedia summary I understand that when the travelers come home and are accused of fabricating the whole thing, one of them tries to "find" this message by running their own computer program. She finds a message, or does she? Is it just a (very unlikely?) statistical fluke? What is noise and what is message when you are dealing with a literally infinitely long string of numbers? (Wasn't this also the plot behind one of Stanislaw Lem's books?).

I guess if he found a message the news would be all over the place by now so he didn't find a message (or maybe he's just keeping the insights to himself for stock market gains like in the movie "Pi"). Anyway, how DO you go about finding patterns in a finite (if you can call 2.7 trillion finite!) string of numbers?

Re:Did he find a message? by InlawBiker · 2010-01-04 20:26 · Score: 1

How could you not?
Re:Did he find a message? by Dahamma · 2010-01-04 20:42 · Score: 2, Funny

Exactly! And hence the discovery of our blessed lady of the grilled cheese sandwich...
Re:Did he find a message? by JustOK · 2010-01-05 01:01 · Score: 1

does it have bacon on it? It there was truly a god, the sandwich would have bacon on it.

--
rewriting history since 2109
Re:Did he find a message? by ettlz · 2010-01-05 01:40 · Score: 2, Funny

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.
Re:Did he find a message? by ceoyoyo · 2010-01-05 02:06 · Score: 2, Interesting

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
Re:Did he find a message? by Stooshie · 2010-01-05 03:30 · Score: 1

"(if you can call 2.7 trillion finite!)"

erm, by definition it is finite!

Interestingly, if someone has 2.7 trillion digits of Pi stored on their hard drive, they could actually have more than just a message. The may, unwittingly, be in possession of material that breaks copyright law! :-)

--
America, Home of the Brave. ... .and the Squaw.
Re:Did he find a message? by mcgrew · 2010-01-05 04:05 · Score: 1

The message was "We apologize for the inconvinience"

--
Free Martian Whores!
Re:Did he find a message? by HeckRuler · 2010-01-05 05:07 · Score: 1

You are not wrong. Pi is irrational and goes on forever, and it does contain every combination possible. Those images will appear in addition to a sequence of 60 1024x800 full-color raster images that show goaste furiously thrusting when you flip through them.
Re:Did he find a message? by John+Hasler · 2010-01-05 14:53 · Score: 1

> The may, unwittingly, be in possession of material that breaks copyright
> law! :-)
Not USA copyright law. It is *COPY*right. Independent invention does not infringe.

--
Warning: this article may contain humor, sarcasm, parody, and perhaps even irony. Read at your own risk.

I'm not impressed - Superman was faster than a by anti-NAT · 2010-01-04 20:38 · Score: 2, Funny

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

Re:So... umm... by msclrhd · 2010-01-04 20:39 · Score: 1

Improving the algorithms for arbitrary precision arithmetic -- that is the area that Fabrice is interested in, not necessarily computing X number of digits of pi. That, and (a) it is interesting, (b) it is a challenge and (c) let's do it for fun.

2.7 trillion digits by asterix_2k1 · 2010-01-04 20:39 · Score: 1

..ought to be enough for everybody.

Re:So.... by Fjodor42 · 2010-01-04 20:49 · Score: 2, Informative

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."

Re:Pattern? by Trepidity · 2010-01-04 20:54 · Score: 2, Interesting

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

Too bad... by hallux.sinister · 2010-01-04 20:54 · Score: 5, Funny

Only another four hundred billion decimal places, and they would have found the last one!

~Hal

Re:Pattern? by Anubis+IV · 2010-01-04 21:02 · Score: 1

It's pi, man. There are no patterns.

Re:Pattern? by Silpher · 2010-01-04 21:15 · Score: 1

So if you would include pi in your fractal equation you'll get a infinite world with infinite diversity?

Re:Pattern? by vorlich · 2010-01-04 21:23 · Score: 1

There's a pattern to be found in everything provided you cut the logos and labels off your black 501's and never, ever enter a Tommy Hilfiger store.

--
Posts, MyBio or Sig, may contain satire, sarcasm, bolded nouns be sardonic or even witty & be Church of SD

fabrice BELLARD by Antiocheian · 2010-01-04 21:24 · Score: 1

Wasn't he the guy who developed lzexe ?

Anyway, what's with surnames spelled in caps ? Does he say "I am fabrice" and then he screams "BELLARD" when stating his name ?

Re:fabrice BELLARD by Anonymous Coward · 2010-01-04 22:22 · Score: 1, Informative

I read something recently on this, it's (apparently) a French convention, presumably to make it clear which name is the surname. I don't know much about it, just something I saw on the Planet Debian RSS:
http://gwolf.org/blog/internationalizing-your-local-customs
Re:fabrice BELLARD by PhunkySchtuff · 2010-01-04 22:29 · Score: 1

http://bellard.org/
He's also the guy who launched ffmpeg and is working on Qemu, among other things...

--
Specialist Mac support for creative pros, Melbourne
Re:fabrice BELLARD by sfsp · 2010-01-05 01:47 · Score: 1

Yes, he developed lzexe, and other stuff.
Using CAPS to designate the surname or family name is common usage in several international communities, especially those that have members which are from cultures which put the family name first.
I have seen it frequently in Esperanto forums.

Anyone tried this on Maple? by Anonymous Coward · 2010-01-04 21:41 · Score: 1, Interesting

Has anyone tried to calculate PI to an ungodly precision on Maple/Mathematica/Mathlab/Macsyma/etc.?

I wonder if it is even possible on a computer of this guy's specs?

I think I've spotted an error by PhunkySchtuff · 2010-01-04 22:23 · Score: 1

On his page with extracts of the digits of Pi, in the third column of the 799,999,951th digits, he's got a 2 where I think it should be a 5.

^_^

--
Specialist Mac support for creative pros, Melbourne

Re:Pattern? by PhunkySchtuff · 2010-01-04 22:24 · Score: 1

Yeah, and if nothing else, watch out for the Michelin Man (Bibendum)

--
Specialist Mac support for creative pros, Melbourne

easy by Tjebbe · 2010-01-04 22:27 · Score: 1

I have just calculated a digit that's much further. It's 7, and it's somewhere around the 8 trillionth decimal. Give or take a few.

Re:So... umm... by JasterBobaMereel · 2010-01-04 23:02 · Score: 4, Informative

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

Would have been nice to see some code. by flimflammer · 2010-01-04 23:04 · Score: 2, Insightful

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.

Re:Pattern? by PRMan · 2010-01-04 23:55 · Score: 1

If you would put the outcomes in a graph would a pattern arise?

When I graphed it, I got a perfect circle...

--
Peter predicted that you would "deliberately forget" creation 2000 years ago...

Re:I guess that's a by Tanuki64 · 2010-01-05 00:00 · Score: 1

I mean, apart from sheer nerd value, this has absolutely no worth to science or humanity.

Are you sure? I did not read the original article. Would be useless since I doubt I would understand the math his program is based on. But when the previous record was done on a multi million dollar machine and he did it on a single desktop computer I think it is not far fetched to assume he must have found some significant improvements to the pi calculating algorithm.

If this is possible for pi calculation, could something like that also be possible for prime number calculations? Maybe someone like him finds a tremendously faster method for prime factorizations? This definitely would affect humanity, when suddlenly a good deal of encryted data can easily decrypted on a cheap standard pc.

PI At Home by pinballer · 2010-01-05 00:31 · Score: 1

I don't get why computation stops at a certain digit? Wouldn't it be possible to keep computing indefinitely and then announce the number of digits at periodic checkpoints? Instead of SETI at Home and Folding at Home what about "PI at home" ??

Re:PI At Home by Kopachris · 2010-01-05 01:28 · Score: 1

Yeah, I think that someone needs to set up a pi computation BOINC project and just keep calculating. The real question is "would it be feasible?" I guess they'd have to go about it a different way than {SETI,Folding}@Home. Instead of giving the client a "chunk" of instructions, you could just give it one digit. The algorithm for finding a particular digit (the BBP or Bellard's formula) could be stored on the client's computer indefinitely, and the computer could simply be instructed to extract a single digit or a block of digits and send them back to the host.
PiHex already did this, sorta, but in binary and only was after specific ranges of digits. I think the main deciding factor would be speed. How many digits can the average computer (or slightly above average, since that's the kind of people who would sign up) compute in about a second? A minute? An hour? Is it linear? We ought to run benchmarks before doing anything like this.

Re:So, how do you calculate Pi? Seriously by mr+exploiter · 2010-01-05 01:23 · Score: 1

You have the force. Use It.

Re:So, how do you calculate Pi? Seriously by Kopachris · 2010-01-05 01:30 · Score: 1

RTFM: http://en.wikipedia.org/wiki/Pi#Computation_in_the_computer_age

I'm building an atomic bomb. by tjstork · 2010-01-05 01:32 · Score: 3, Funny

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.

agreed by JeanBaptiste · 2010-01-05 01:39 · Score: 1

I plugged his number into my circle-generator and it created a cube.

I calculated pi to the last digit... by stox · 2010-01-05 01:48 · Score: 3, Informative

in base pi. The answer was 10.

--
"To those who are overly cautious, everything is impossible. "

No ECC RAM! by Zemplar · 2010-01-05 01:50 · Score: 1

From TFA's technical notes: "Unfortunately, the RAM had no ECC (Error Correcting Code), so random bit errors could not be corrected nor detected. Since the computation lasted more than 100 days, such errors were likely [12]."

Great we have all these digits, but they're mostly useless bits and their reliability is suspect.

Euler's identity by AlpineR · 2010-01-05 01:59 · Score: 1

Forget the radius. Now I can calculate zero to 2.7 trillion digits of precision: pow(e,i*pi)+1=0

Re:So... umm... by mcgrew · 2010-01-05 03:18 · Score: 1

Well, 'til now I saw the Pi-calculating e-peen waving as something like basic research. Ya know, where you build better computers and then you don't find anything sensible to do with them, so let's have them, say, find the next big prime (ok, being in cryptography I can see an application for that...)

Threads like this one make me feel incredibly stupid.

Could someone fill me in what purpose that may be?

The same purpose as climbing a mountain -- because it's there.

--
Free Martian Whores!

Re:So... umm... by rafaelolg · 2010-01-05 03:25 · Score: 1

Now quantum mechanics and so most of modern electronics uses it ....

Errr...therefore it is still useless.

Re:Pattern? by Stooshie · 2010-01-05 03:33 · Score: 1

As trepidity just said, it has not been proven that there are no patterns.

--
America, Home of the Brave. ... .and the Squaw.

...and they're needing to hand-verify for accuracy by kjcole · 2010-01-05 03:44 · Score: 1

Meanwhile a machine in Redmond expects to complete the task sometime around the year 2518... (After 8 years it is now out to 15 places after the decimal.)

The last digit by RogueWarrior65 · 2010-01-05 03:47 · Score: 1

Is zero. You can stop now.

Thumbs Up, Fabrice! by cfriedt · 2010-01-05 04:07 · Score: 2

Fabrice Bellard continues to amaze me.

Well, shit, *I* could do THAT! by Xenophon+Fenderson, · 2010-01-05 04:20 · Score: 1

Of course, I'm not sure if I would bother with making my calculation accurate after the first fifty or sixty digits, though. ;)

--
I'm proud of my Northern Tibetian Heritage

A thought by marqs · 2010-01-05 04:36 · Score: 1

Why not use PI as radix?
Then we could all have the joy of finding unlimited decimal to all of our everyday counting :)
Guess you could count just fine from 0 to 3. Perhaps a bit longer if my calculations are correct
3.1 ~ 3 + 1/pi^2 pi so there the problems start.

Now imagin the hassel to work out if you can fit four passengers in your car...

Pi digits to the e*trillion? by CodeDragonDM · 2010-01-05 08:46 · Score: 1

Am I reading that right that e accurate to two places, times a trillion is the number of places that pi has been calculated to? Nice. I see the answer to the Pi versus e debate has a tangental answer.

Wrong. Computers can make mistakes. by nuckfuts · 2010-01-05 10:04 · Score: 1

A correct algorithm is not enough to ensure a correct result.

The fact is that binary digits in RAM can (and do) spontaneously change from 0 to 1 and vice-versa. A few possible causes are listed here. The likelihood of such errors increases with the number of digits involved.

There is no mention of whether Bellard used ECC RAM.

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New Pi Computation Record Using a Desktop PC

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