What is the 100th trillion digit of PI decimal point? Google gives the answer with Debian server

Arrangement | Su mi

Produce | CSDN（ID：CSDNnews）

π=3.1415926......

Must have been a student , When it comes to reciting pi π The number after the decimal point , Many people's desire to win or lose is quietly aroused ,“ The more you recite, the more powerful you become ” Our views are also deeply rooted in our minds .

Little imagine , In Mathematics 、 The scientific community , This view still exists , But at this time, the competition has already changed from human brain to cloud computing .

In recent days, , come from  Google Cloud The developer of the  Emma Haruka lwao It breaks the calculation π Worth a new world record , It can transform π  The value of is calculated until 100 Trillions , Pass the verification , The first 100 The decimal point value of trillion is 0.

Regarding this ,Google The team sent a text to celebrate ,“ Records are meant to be broken .”

Google How to calculate 100 Trillions π decimal point ？

Review the industry's π A contest on a decimal value , Seems to have entered a state of anxiety in recent years , The record breaking time is getting shorter and shorter .

2019 year ,Google take  π The decimal point is calculated to 31.4 Trillions , Set the world record of that year .

2021 year , Scientists at the University of Applied Sciences in the state of graupenden have calculated another 31.4 Trillion bit constant , Make the total number reach the number after the decimal point 62.8 Trillions , Break the world record .

2022 year 3 month , stay Google Use... For the second time Google Cloud After calculating , It will be after the decimal point 100 Trillions have been calculated .

Less than... Were used in this project  158 Time of day , More precisely , It should be used 157 God 23 Hours 31 branch 7.651 second .

When we have a deeper understanding of Google How to calculate 100 Trillions π At the decimal point , It shows us the technology behind ：

• Program ： It uses  Alexander J. Yee One of them is called y-cruncher v0.7.8（http://www.numberworld.org/y-cruncher/） The program completed heavy work

• Algorithm ： Chudnovsky algorithm （https://arxiv.org/abs/1809.00533）

The primary computing node is a running Debian Linux Of n2-highmem-128 machine , use 128 individual vCPU、864GB RAM, And support 100Gbit/sec The exit bandwidth of . in addition ,Google Created a networked storage cluster , because n2-highmem-128 Provides... For a single virtual machine 257TB Additional storage for , And the temporary storage required for its estimated calculation needs at least 554TB.

Each storage server is a n2-highcpu-16 Computer , There are two configurations 10,359 GB Region balanced permanent disk .N2 The machine family offers a balanced cost performance , When configuring 16 individual vCPU when , Can provide 32 Gbps Network bandwidth , And you can choose to use the latest Intel Ice Lake CPU platform , This makes it a good choice for high-performance storage servers .

Pass benchmark ,Emma Haruka lwao  The final calculation is π The hundredth trillion digit of is 0. thereafter , It also uses another method called Bailey-Borwein-Plouffe The formula algorithm is verified .Emma Haruka lwao Express ,“ This verification is the most terrible moment in the whole process , Because five months after the start of the calculation , There is no definite way to know whether the calculation is successful . It is gratifying that ,Bailey-Borwein-Plouffe The formula shows that our result is valid . " ！”

Here is the final result 100 Digit number ：

What's the point of counting so many decimal points ？

After verification , There is no doubt that the result is correct . However , Many netizens have also questioned , It takes so much trouble to figure out π What is the meaning of value ？

CSDN Pay to download from visual China

Regarding this , Foreign media The Register Also on the Google The cost of this project has been estimated ：

n2-highmem-128 The price of the machine is per hour 7.706976 dollar , Therefore, the cost of computing server is about 29,000 dollar .

n2-highCPU-16 The cost of the instance is per hour  0.57 dollar , That is, the cost of the whole operation is about 70000 dollar . Besides , Data mobility will greatly increase this task .

And these costs are calculated to π Medium 100 Trillions .

however , stay Google In my opinion , It's worth it together .Iwao Point out in the blog post ,“ This large-scale calculation proves Google Cloud How our flexible infrastructure enables teams around the world to break through the boundaries of scientific experiments . This is also an example of the reliability of our products —— The program has run for more than five months without node failure , And correctly handled 82 PB disk I/O Each bit in . In the past three years , Improvements in our infrastructure and products have made this calculation possible .”

besides ,Google The script code of the automation solution used in this calculation is also included in GitHub（https://github.com/GoogleCloudPlatform/pi-delivery/tree/main/pi-100t） Open source , Interested students may wish to have a deeper understanding of the code .

Reference link ：

https://cloud.google.com/blog/products/compute/calculating-100-trillion-digits-of-pi-on-google-cloud

https://www.theregister.com/2022/06/09/google_100_trillion_digits_of_pi/?td=rt-3a