Pi calculation smashes records

January 7, 2010 by Lin Edwards report

(PhysOrg.com) -- A computer scientist in France has broken all previous records for calculating Pi, using only a personal computer. The previous record was approximately 2.6 trillion digits, but the new record, set by Fabrice Bellard, now stands at almost 2.7 trillion decimal places.

Bellard, of Paris Telecom Tech, made and checked the calculation by running his own software algorithms for 131 days. The previous record calculation, set by Daisuke Takahashi at the University of Tsukuba in Japan in August 2009, took only 29 hours to complete, but used a super-computer costing millions of dollars, and running 2000 times faster than Bellard's PC.

Pi is the value of the ratio of the circumference of a circle to its diameter, and has been of interest to mathematicians for hundreds of years, since Sir developed formulae to extend the number of decimal places.

Bellard has been following the records for calculating Pi to the maximum number of decimal places since he received his first book about Pi at the age of 14. Computations to find a value to any number of decimal places are part of a branch of mathematics called "arbitrary-precision arithmetic". For Bellard the calculation was more for fun than because of an obsession with the digits, but he said that arbitrary-precision arithmetic has applications because it can be used for testing algorithms and computers. He claims his method is about 20 times more efficient than previous methods.

Bellard said he used the Chudnovsky formula to produce a binary result (a process that took 103 days), which was then checked (which actually took 34 hours on 9 computers, but would have taken 13 days on one PC), and converted to a base-10 result (12 days), which was then verified (3 days).

Bellard's computer cost less than €2000 (roughly $2870 US) and ran Linux's Red Hat Fedora operating system. It had a Core i7CPU at 2.93 GHz, and had 6 GB of RAM and 7.5 TB of disk storage space in five 1.5 TB hard disks. He wrote all the required software.

The world record for memorizing and reciting Pi was set in 2005 by a Chinese graduate student, Lu Chao, who spent a year learning 100,000 digits and was able to recite Pi to the 67,890th decimal place before he made an error. The feat took just over 24 hours. Reciting Bellard's result of 27 trillion digits would take over 1,284,000 years at the Guinness Book of Records' required rate of one digit every 15 seconds.

M Bellard is perhaps best known as the writer of the open source project FFmpeg and processor emulator QEMU. He said he has no immediate plans to calculate Pi to further digits in the future, but may do, depending on his motivation and the availability of larger and faster storage. He intends to release open-source versions of his software for Linux and Windows to enable anyone who is interested in furthering the calculation to beat him to it.

Explore further: A trillion triangles: New computer methods reveal secrets of ancient math problem

More information: bellard.org/pi/pi2700e9/

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1 / 5 (2) Jan 07, 2010
He wrote all the required software.
Of course. But which language? Certainly not C++.
not rated yet Jan 07, 2010
if he wrote it using fedora... probably python.
not rated yet Jan 07, 2010
He wrote it in C, or at least he gives C source here;

... and seems to prefer C programming in general.

4.5 / 5 (2) Jan 07, 2010
Actually it was probably C or C++

He did this on one computer and the algorithm produced an arbitrarily long float. besides the fac that the data structure is HUGE ... the memory management to make it effecient is most easily done in a low level language like C or C++, granted python is C based I think it is clumsy, like using a chainsaw when you need a scapel. You can do it but its almost easier in C.

- I am biased - I work as a C programmer.

as i was writing the other statement came up
-- i love the edit feature
1 / 5 (2) Jan 07, 2010
Nobody ever heard of Fortran? Fascinating.
4 / 5 (4) Jan 07, 2010
Lots of people have heard about Fortran frajo, but arbitrary precision arithmetic requires handling raw memory storage and bit twiddling. A language like Fortran is quite constrained in this respect, and doesn't offer any advantages to compensate.

I think that there are really only 3 choices, assembler, C, or C++. For a specialized application of this sort, I would probably attempt to use a nvidia type DSP graphics card for the heavy duty computational load, programming that part in DSP microcode( assembler). High end graphics cards offer (by far), the highest amount of computational power per buck. I would program the rest in C or C++ because those languages offer metal level access to the computing engine without the complications and complexity of assembler.
5 / 5 (1) Jan 07, 2010
bellard@home? Modify the source of that software to work with a seti@home plug-in.
not rated yet Jan 07, 2010
Feh. Thanks Andreas for posting that. I for one believe in Conspiracy of the very highest sort but I also believe it doesnt involve esoterics or metaphysics except for aesthetic and political purposes. I believe for instance that the bible code is pure statistical coincidence (though wierd as hell), and that numerology is probably the same. I hope 'feh' isnt an insult in some language I dont know. And to all the four-eyed literalists here who like to 1 us schizoid conspiracy delusionists I say- Bite me.

This is sad- it pays to stay in touch!
4 / 5 (1) Jan 07, 2010
and exactly what was the point of this colossal waste of resources?
Jan 08, 2010
This comment has been removed by a moderator.
3 / 5 (2) Jan 08, 2010
And to all the four-eyed literalists here who like to 1 us schizoid conspiracy delusionists I say- Bite me.
Isn't that your preferred treatment?
not rated yet Jan 08, 2010
And to all the four-eyed literalists here who like to 1 us schizoid conspiracy delusionists I say- Bite me.
Isn't that your preferred treatment?

Only based on the perceived merits of the individual quote dearie.
Jan 11, 2010
This comment has been removed by a moderator.
1 / 5 (1) Jan 11, 2010
given the limited precision with which digits are represented in any programming language can the results be trusted out to a 1000 digits let alone a trillion?
See http://en.wikiped...ithmetic

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