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17 Sep 2010

A researcher has calculated the 2,000,000,000,000,000th digit of pi - and a few digits either side of it.

Nicholas Sze, of technology firm Yahoo, determined that the digit - when expressed in binary - is 0.

Mr Sze used Yahoo's Hadoop cloud computing technology to more than double the previous record.

The computation took 23 days to complete on 1,000 of Yahoo's computers.

The heart of the calculation made use of an approach called MapReduce originally developed by Google that divides up big problems into smaller sub-problems, combining the answers to solve otherwise intractable mathematical challenges.

At Yahoo, a cluster of 1,000 computers implemented this algorithm to solve an equation that plucks out specific digits of pi.
Pi slicing

The pursuit of longer versions of pi is a long-standing pastime among mathematicians.

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 at 2.7 trillion digits.

Instead, each of the Hadoop computers was working on a formula that turns a complicated equation for pi into a small set of mathematical steps, returning just one, 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," Mr Sze explained to BBC News.

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

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

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

Mr Sze added that the calculation was also a good test for the Hadoop hardware and approach.

"This kind of calculation is useful in benchmarking and testing," he said.

"We have used it to compare the [processor] performance among our clusters."


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