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New cloud computing algorithm successfully computes two-quadrillionth digit of pi
Using a handy algorithm that splits a calculation into thousands of little intermediary processes, a researcher at Yahoo has used a cluster of 1,000 computers to calculate the 2,000,000,000,000,000th digit of pi. Not all two quadrillion digits -- just that one digit (which is a binary 0, if you're wondering).The calculation was made possible by Hadoop, an open source implementation of Google's extensively-used MapReduce. Yahoo is now also presumably working on something that will make use of it (but considering Bing now powers Yahoo search, I'm not quite sure what they'd be using it for!)
As for whether the 2,000,000,000,000,000th digit of pi actually has a use, I'll leave as an exercise to you guys. Incidentally, earlier this year, pi was calculated to 2.7 trillion digits on a normal desktop PC!
Comments
7
Subscribe to commentshmmSep 18th 2010 10:50AM
It was calculated in binary. I could have guessed it and there would have been a 50% chance of me being correct!
The algorithm was such that to calculate in decimal, all previous digits would have been needed, which again is a hard task. It could only have been calculated in bases which are a power of 2 such as 2, 4, 8 ,16, etc.
Sebastian AnthonySep 18th 2010 1:03PM
I'm glad someone understands how it works :) Thanks for the clarification.
DarakSep 18th 2010 1:00PM
This article needs a wee bit of clarification: Did he calculate the 2 quadrillianth binary digit of pi, or the 2 quadrillianth decimal place of pi? There's a substantial difference between the two of them, and it doesn't take a math whiz to figure out that a binary 0 doesn't give you the decimal digit by itself.
Reading the source article it's simple to figure out, but not this DLS version.
Sebastian AnthonySep 18th 2010 1:06PM
Honestly, I'm not sure. It's a bit over my head.
But I'm glad the source article clarifies things :)
DarakSep 18th 2010 1:34PM
I'll try to break it down a bit:
Essentially, just like you can represent fractions in decimal with numbers after the decimal point (ie, 3/4 = .75), you can do the same in binary. It just changes the value of what's after the binary point. Instead of being 10 ^ -1 (tenths) and 10^-2 (hundredths), etc, it becomes 2^-1(halves) and 2^-2 (quarters) and so on. Thus the earlier 3/4 is now .11.
Obviously this fraction has the same length in decimal and in binary, but most do not, especially long ones. Hence why there's a difference in precision between the 2 quadrillianth decimal place and the 2 quadrillianth binary place.
Source seems to indicate it was calculating the 2 quadrillianth binary place, which makes sense since the answer given was 'binary 0" and you can't tell what the decimal value at that place is from a single binary digit.
hmmSep 18th 2010 2:09PM
Yes, it is the two quadrillionth bit, or the 2 quadrillionth digit when pi is expressed in binary and not when it is in decimal.
ColorblindMonkSep 20th 2010 12:43PM
Now that's a big piece of Pi!