The new HPC system at the Graubünden University of Applied Sciences is now occupied with complex research tasks – but for the past few months, it’s had its fingers in other πs. After 108 days of calculation, the system has calculated π to upwards of 62.8 trillion digits, besting the previous record of roughly 50 trillion digits by 12.8 trillion in less than half the calculation time.
The university’s system, equipped with a terabyte of memory, is also powered by a pair of AMD Epyc 7542 CPUs and supplemented by 38 16TB hard drives. The researchers explained that they opted for hard drives, versus solid state drives, due to the nature of the π calculation.
“We [expected] a large number of write cycles for the π calculation and future calculations, which results in high wear and tear on SSDs,” the researchers explained (in translation). “Since the storage prices for SSDs are also five to ten times higher than for conventional HDDs, we decided on HDDs in the design process. However, this only affects the memory space for the calculations. We use SSDs for the installation of the operating system, since fewer write cycles occur here and the storage space requirement is in the range of a few GB.”
Even with that amount of RAM and storage space, the researchers said that such a system would “only be sufficient for a calculation of a few hundred billion digits.” To allow the system to go beyond that limit by several orders of magnitude, they used a program called y-Cruncher to offload work from the RAM onto the hard disks, a technique called “swapping.” Further, they configured y-Cruncher to enable parallel access to the swap space in order to compensate for the slower read-write speeds on the hard disks, enabling an overall transfer speed on the order of 8.5GB/s.
During the calculation process, the researchers devoted 310TB of the storage space for swapping and nearly 180TB for backing up the cached calculation data. The final calculation of π, which measured 62,831,853,071,796 digits, itself took up 63TB of storage.
The researchers began their quest to beat the world record for calculating π on April 28, 2021, when the calculations began. On August 4th, the researchers successfully calculated π to 62.8 trillion digits in hexadecimal, and a week later, they had converted the hexadecimal form to a decimal form. On August 14th, 108 days after they began, they announced the completion of the calculation.
The previous record-holder was Timothy Mullican, who calculated 50 trillion digits of π over 303 days beginning in April 2019, who himself was preceded by Google, which calculated over 31 trillion digits of π over 121 days beginning in September 2018. “We want to show that we can efficiently carry out the extremely memory-intensive calculation of π to 62.8 trillion digits with a limited budget, hardware and human resources,” the Graubünden researchers wrote.
The last ten known digits of π are now 7817924264.