Google Smashes Pi Record For Pi Day
Written by Sue Gee   
Thursday, 14 March 2019

To mark this year's Pi Day, Google has announced a new world record of 31.4 trillion digits for our favorite irrational mathematical constant, Pi. 

March 14 is celebrated as Pi Day because it is represented by 3.14 - the first three digits of a fundamental mathematical constant that has the mystery characteristics of being transcendental and irrational. If you want to know more about its properties see Transcendental Pi And The Transfinites by Mike James. 

The previous Guinness World Record for the most accurate value of Pi was set by Peter Trueb in 2016 with 22.4 trillion digits. This has now been convincingly overtaken by Google's Emma Haruka Iwao who computed 31,415,926,535,897 decimal digits, which is  26,090,362,246,629 hexadecimal digits.

If you want details of the method these are supplied in a Pi Day blog post by Alexander Yee who explains that the computation used the Chudnovsky formula and took 121 days beginning on September 22, 2018 and ending on January 21, 2019. Verification was done twice using Bellard's 7-term BBP and the original 4-term BBP formulas. These were run in December and took 20 and 28 hours respectively. Both the computation and verification runs were done using y-cruncher v0.7.6.

The statistics are included in this screen dump:

Yee Pi Screen

Source:Alex Yee blog

(click to enlarge)

The importance to Google of the achievement of 3.14 trillion digits is that this is the first time that the record has been broken using the cloud. As Emma Haruka Iwao claims in her blog post Pi in the sky, it proves Google Cloud’s infrastructure works reliably for long and compute-heavy tasks. In this video, which has the title , "A recipe for beating the record of most-calculated digits of pi." Emma Haruka Iwao outlines how and why she set out to beat the world record. 

The video lasts for 3 minutes and 14 seconds (notice the Pi theme), which is rather more than is required, and the closed captions can be very misleading. For example, she says had been told by her Computer Science professor, himself a former world record holder for digits of Pi, that, to paraphrase slightly, from an engineering standpoint there is no need for trillions of digits of Pi and that 20 to 30 digits are sufficient. At this point I couldn't make out the "for what" bit of the sentence. The captions read:

he said from ensuring some point its not really useful to have chilled of digits of pi because you probably need up to 2030 digit to send water through space...

The sentiment that a couple of score of digits of Pi are all that we could possibly need had already been aired in a Pi Day post from 2017. In How many digits of pi do we really need? Brad Plumer cited Marc Rayman, the director and chief engineer for NASA's Dawn mission as saying that NASA, which certainly requires accuracy, doesn't need trillions of digits and that NASA uses just 15 - 3.141592653589793 which could result in an error of 1.5 inches in a circumference of a 25 billion mile circle.

According to Rayman, with 40 digits of Pi, you could calculate the circumference of the entire visible universe — an area with the radius of about 46 billion light-years:

"to an accuracy equal to the diameter of a hydrogen atom." 

Plumer noted:
Mathematicians have been able to calculate 40 digits of pi since the 1700s. Ever since then, they've been rocketing far beyond our wildest spaceship needs:

Emma's rejoinder would be that from a computer software point of view it is interesting to have more digits - and certainly as a Google Cloud Developer Advocate's point of view Pi is great for promotion and marketing. 

In her blog post: 

Using Compute Engine, Google Cloud’s high-performance infrastructure as a service offering, has a number of benefits over using dedicated physical machines. First, Compute Engine’s live migration feature lets your application continue running while Google takes care of the heavy lifting needed to keep our infrastructure up to date. We ran 25 nodes for 111.8 days, or 2,795 machine-days (7.6 machine-years), during which time Google Cloud performed thousands of live migrations uninterrupted and with no impact on the calculation process.

Running in the cloud also let us publish the computed digits entirely as disk snapshots. In less than an hour and for as little as $40/day, you can copy the snapshots, work on the results, and dispose of the computation resources. Before cloud, the only feasible way to distribute such a large dataset was to ship physical hard drives.

Then there are the general benefits of running in the cloud: availability of a broad selection of hardware, including the latest Intel Skylake processors with AVX-512 support. You can scale your instances up and down on demand, and kill off when you are done with them, only having paid for what you used.

Her blog post also gives details of how customers can use the service, essentially to play and experiment with digits of Pi at the rate of  $40 per day.

Happy Pi day.


More Information

Pi in the sky

A recipe for beating the record of most-calculated digits of pi

Google Cloud Topples the Pi Record

How many digits of pi do we really need? Eh, not that many, says NASA. service

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