Estimating π using MapReduce

I am taking a class ray ban sunglasses called Senior Seminar in which we ray ban outlet needed to give a talk about a technical subject. I wanted my talk to be unique, so I thought about doing some research about concurrency performance on mobile devices versus PCs. Quickly I decided this was fairly boring, since I could see Wholesale Jerseys the conclusion coming from cheap jerseys a mile away: concurrency works a lot better on PCs than on mobile devices.sports74.ruMountains Photo

I was using the calculation of π as a CPU-bound workload for this testing, so I decided to pivot on this. In particular, how can concurrency help with the computation of π? I found the Wholesale Jerseys paper “The BBP Algorithm for Pi,” by David H. Bailey, which gave me a detailed description of a good way forward. Since I’m interested in finding new ways to use <a href="http://en.wikipedia .org/wiki/MapReduce”>MapReduce, I decided to implement the ideas of the paper inside a small MapReduce job. This paper details a method for computing a handful of hexadecimal digits starting at a certain place after the decimal point. For some n number of digits requested, I apply this method repeatedly to get the digits from 0 through n. Each call to map() generates one handful of digits (currently set to 5). The further this handful is from the decimal point, the more time it takes to generate. Unfortunately, this means the total running time grows geometrically. On a high-performance Hadoop cluster, calculating 100,000 digits took 31 seconds. This is not coming close to breaking any records, and is probably slower than you could do on your personal computer by using a more efficient (but less distributed) algorithm. Nonetheless, this was a very educational project.

The source code for the project is available on my GitHub. The results of computing the first 100,000 digits are also available.

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