21. November 2016

Pi computed to 22.4 trillion digits


How big is pi? Most high school students will shoot off 3.14 without much thinking, but Peter Trüb, software developer at DECTRIS, has a different answer. According to his calculation, which came to a conclusion last week, pi weighs in at 8.5 TB. Calculated to 22.4 trillion digits, "pi is so long it would fill a library of several million 1000-page books if printed on paper", says Trüb.

There are several reasons for calculating pi to ever increasing precision. Mathematicians would like to find out whether pi is normal. If so, each sequence of digits would be equally likely to occur, and the stream of digits would appear perfectly random. Computer scientists use pi to test numerical analysis algorithms. For DECTRIS, the point of the calculation was the massive stressing of a computer system similar to those under development for EIGER detector control and data processing.

We used a DELL PowerEdge 930 server with four hyper-threaded 18-core Intel Xeon CPUs and a total of 144 parallel threads. The system memory was 1.25 TB, but the critical point for the success of the calculation was the performance of the disks. Swiss electronics distributor Brack.ch supplied twenty-four 6 TB hard drives to hold the vast amounts of data generated during the calculation and backups of intermediate results. Always eager to support their customers in special projects, Brack.ch recommended Seagate Enterprise Capacity hard disks for their high data transfer rates and 24/7 reliability. In the end, more than 7 PB of data were read and written over the course of the project, filling each hard drive sixty times over without a glitch.

The calculation of pi with Alexander J. Yee's highly parallelized program γ-cruncher put a heavier strain on our hardware than even macromolecular crystallography experiments with the largest EIGER detectors. Swapping of pages from memory to disk caused high sustained data transfer rates, while the server ran at full CPU load for extended periods of time. "While the hard drives were specifically chosen for this test, it revealed the kind of system reliability that our customers have come to expect of DECTRIS systems", says Stefan Brandstetter, Head of Product Management at DECTRIS. The calculation proceeded without unexpected interruption and finished in 105 days.

With this calculation, DECTRIS has not only set a new world record for the precision of pi but, says Clemens Schulze-Briese, CSO of DECTRIS, also "performed a veritable stress test on a system similar to those some of our customers will encounter as DCU of their latest EIGER X 9M and EIGER X 16 detectors". The server has passed this test with flying colors, to the benefit of mathematicians and crystallographers alike.

If you are interested in obtaining all 22.4 trillion digits of pi, please contact info@dectris.com. Peter Trüb describes the pi project in more detail in his personal blog.