Python implementation of π digits calculation using Chudnovsky algorithm. This method is one of the most efficient way to calculate π and was used multiple times in breaking world record of π digits calculating.
Performance tests showed that the time complexity of the implementation of the algorithm is square. Increase presents how much execution time has raised compared to previous test. The implementation is able to calculate 1 milion digits under 8 minutes.
# powers of 2 test command
python test.py --max 20
# powers of 10 test command
python test.py --dec --min 1 --max 6
Powers of 2
digits: 1024 time: 0.523 ms increase: None
digits: 2048 time: 1.792 ms increase: 3.427
digits: 4096 time: 6.922 ms increase: 3.863
digits: 8192 time: 25.601 ms increase: 3.699
digits: 16384 time: 91.741 ms increase: 3.583
digits: 32768 time: 377.478 ms increase: 4.115
digits: 65536 time: 1.599 s increase: 4.236
digits: 131072 time: 6.742 s increase: 4.216
digits: 262144 time: 28.286 s increase: 4.196
digits: 524288 time: 1.982 m increase: 4.205
digits: 1048576 time: 8.36 m increase: 4.218
Powers of 10
digits: 10 time: 0.009 ms increase: None
digits: 100 time: 0.022 ms increase: 2.447
digits: 1000 time: 0.38 ms increase: 17.14
digits: 10000 time: 36.527 ms increase: 96.114
digits: 100000 time: 3.913 s increase: 107.114
digits: 1000000 time: 7.6 m increase: 116.546
Powers of 2
digits: 1024 time: 0.688 ms increase: None
digits: 2048 time: 1.685 ms increase: 2.449
digits: 4096 time: 6.751 ms increase: 4.006
digits: 8192 time: 27.759 ms increase: 4.112
digits: 16384 time: 116.173 ms increase: 4.185
digits: 32768 time: 491.369 ms increase: 4.23
digits: 65536 time: 2.076 s increase: 4.226
digits: 131072 time: 8.813 s increase: 4.245
digits: 262144 time: 37.879 s increase: 4.298
digits: 524288 time: 2.638 m increase: 4.178
digits: 1048576 time: 11.16 m increase: 4.231
Powers of 10
digits: 10 time: 0.035 ms increase: None
digits: 100 time: 0.024 ms increase: 0.689
digits: 1000 time: 0.438 ms increase: 18.02
digits: 10000 time: 44.101 ms increase: 100.638
digits: 100000 time: 5.126 s increase: 116.235
digits: 1000000 time: 10.134 m increase: 118.621
Powers of 2
digits: 1024 time: 1.243 ms increase: None
digits: 2048 time: 4.173 ms increase: 3.358
digits: 4096 time: 15.679 ms increase: 3.757
digits: 8192 time: 62.247 ms increase: 3.97
digits: 16384 time: 259.258 ms increase: 4.165
digits: 32768 time: 1.11 s increase: 4.28
digits: 65536 time: 4.641 s increase: 4.182
digits: 131072 time: 19.59 s increase: 4.221
digits: 262144 time: 1.411 m increase: 4.322
digits: 524288 time: 5.868 m increase: 4.158
digits: 1048576 time: 24.996 m increase: 4.26
Powers of 10
digits: 10 time: 0.072 ms increase: None
digits: 100 time: 0.077 ms increase: 1.062
digits: 1000 time: 1.137 ms increase: 14.765
digits: 10000 time: 99.194 ms increase: 87.241
digits: 100000 time: 11.508 s increase: 116.015
digits: 1000000 time: 22.854 m increase: 119.154
Endpoitns that returns digits of π.
Endpoint: https://serverless.wblz.xyz/pi/digits/<count_of_digits>
count_of_digits - how many decimal places of π you want to get (max 1 milion).
Response for https://serverless.wblz.xyz/pi/digits/10:
{
ok: true,
pi: "1415926535"
}
Endpoint: https://serverless.wblz.xyz/pi/range/<from>/<to>
from - starting index of the range of digits you want to get
to - ending index of the range of digits you want to get (max 1 bilion)
Max range size is 1 milion
Response for https://serverless.wblz.xyz/pi/range/5/10:
{
ok: true,
pi: "26535"
}
Run the testing commands on your CPU and share your results creating a PR to this readme if the CPU is not present here yet.