Calculating the number Pi has always captured mathematicians’ interest. This high-performance computer just took the challenge one step further.
A team of Swiss researchers are claiming that their high-performance computer has added 12.8 trillion new digits to the number Pi, in a calculation that reached a record-breaking 62.8 trillion figures in total.
Based at the University of Applied Sciences of the Grisons’s center for data analytics, visualisation and simulation (DAViS), the high-performance computer completed the Pi calculation with a precision of exactly 62,831,853,071,796 digits, smashing the previous record of 50 trillion digits achieved by Timothy Mullican last year.
Before Mullican, the trophy was held by none other than Google, whose team found over 31.4 trillion digits for Pi in 2018.
The Swiss team obtained the result in just over 108 days – that is, three and a half times faster than Mullican, who reached the previous record in 303 days – and is now awaiting verification before it can be entered into the Guinness World Records. Only then will the entire number be made publicly available, but the researchers teased that the last ten known digits of Pi now are: 7817924264.
For most people, the number Pi will only bring back distant memories of math classes, where it was described as the ratio of the circumference of a circle to its diameter, and often shortened to its first few digits: 3.1415.
For centuries – in fact, as early as the ancient Babylonians – mathematicians have been trying to calculate the digits of Pi with as much accuracy as possible. But with the number Pi being known as an irrational number, meaning that it can never be represented with ultimate precision, the point isn’t exactly to find practical uses; rather, the calculation has become an unofficial benchmark for high-performance computing, and an opportunity for scientists to compete against one another.
“We wanted to achieve several goals with the record attempt,” said Heiko Rölke, the head of DAViS. “In the course of preparing and performing the calculations, we were able to build up a lot of know-how and optimize our processes. This is now of particular benefit to our research partners, with whom we jointly carry out computationally intensive projects in data analysis and simulation.”
DAViS’s researchers used a well-established algorithm called the Chudnovsky formula, which was developed in 1988 and is considered the most effective method to calculate the number Pi. Google’s team and Mullican also used the Chudnovsky algorithm.
The algorithm was run thanks to another popular computer software program, y-cruncher, that was designed in 2009 by American developer Alexander Lee specifically to compute Pi.
One of the main challenges, according to the Swiss team, was the amount of memory that was needed to achieve such a large calculation. DAViS’s high-performance computer was set up with two AMD Epyc 7542 processors coupled with 1TB of RAM, which isn’t sufficient to hold all of the digits they were aiming to come up with. The y-cruncher program, therefore, was used to swap out the digits to an additional 38 hard disk drives (HDD) with a total 16TB of storage space, saving a large part of the RAM on the HDDs.
During operation, the computer and the disks could reach up to 80°C, which is why the system was housed in a server rack with constant air cooling to avoid overheating. This contributed over half of the total 1,700 watts of power that the scientists estimate was required for the full calculation, which would still place the system in 153rd position on the Green500 list.
It is unlikely that Pi’s extra 12.8 trillion digits will be used for any practical applications any time soon; the achievement is rather a reflection of scientific ingenuity and high-computing performance.
The Chudnovsky formula, for example, is known for its complexity: when implementing the algorithm, scientists find that the time and resources necessary to calculate the digits increase more rapidly than the digits themselves, while it becomes more difficult to survive hardware outages as the computation increases.
For the Swiss researchers, the new achievement is a reflection of the capabilities of high-performance computing systems, and their potential for other research areas. “The calculation showed that we are prepared for data and computing power-intensive use in research and development,” said Thomas Keller, project manager at the University of Applied Sciences of the Grisons. “The calculation also made us aware of weak points in the infrastructure, such as insufficient back-up capacities.”
DAViS supports the use of high-performance computing in machine learning, for example, in a project called Translaturia that is building a computer-aided tool to translate from the Romansh language, spoken predominantly in the Swiss canton of the Grisons and currently at threat of disappearing.
The computing center is also looking at applications of DNA sequence analysis in allergy and asthma research, which also calls for high-performance computing systems. The new record helps prepare the groundwork for future practical applications.