September 17, 2010

New Pi Record Calculated To The Two-quadrillionth Digit

A researcher working for technology firm Yahoo has calculated the 2,000,000,000,000,000th digit of pi, more than doubling the previous record.

Nicholas Sze used Yahoo's Hadoop cloud computing technology to come up with the unimaginable figure. The computation took 23 days using 1,000 Yahoo computers, racking up the equivalent of more than 500 years of efforts from a single computer.

The core of the calculation made use of an approach called MapReduce -- originally developed by Google -- that divides up few big problems into several smaller problems. It then combines the answers to solve otherwise difficult mathematical equations.

Mathematicians have made it a long-standing pastime to deduce longer versions of pi. But this approach is very different from the full calculation of all of the digits of pi, the record for which was set in January, with 2.7 trillion digits.

Instead, each of the Hadoop computers was working on a formula that turns complicated equations for pi into a small set of mathematical steps and then returns a single specific piece of pi.

"Interestingly, by some algebraic manipulations, (our) formula can compute pi with some bits skipped; in other words, it allows computing specific bits of pi," Sze explained.

Fabrice Bellard, who announced the full calculation in January, told BBC News that the single-digit and full pi calculation are very different in the degree to which they can be broken up into manageable pieces among different computers.

The current, single-digit record is "more a demonstration of the Hadoop parallelization framework... it can demonstrate the power of new algorithms which could be useful in other fields," said Bellard.

The MapReduce approach is useful in physics, cryptography and data mining, he said.

Sze added that the calculation was also a good test for the Hadoop hardware and approach. "We have used it to compare the [processor] performance among our clusters."


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