https://github.com/lzyrapx/pi-miniature-calculation
☕️ A Miniature Program
https://github.com/lzyrapx/pi-miniature-calculation
algorithm
Last synced: 3 months ago
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☕️ A Miniature Program
- Host: GitHub
- URL: https://github.com/lzyrapx/pi-miniature-calculation
- Owner: lzyrapx
- Created: 2018-04-23T10:59:15.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2018-05-02T06:35:55.000Z (over 7 years ago)
- Last Synced: 2025-06-01T23:41:19.908Z (4 months ago)
- Topics: algorithm
- Language: C++
- Homepage:
- Size: 437 KB
- Stars: 1
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Pi-Miniature-Calculation
### 1. Main algorithm ：[Chudnovsky algorithm](https://en.wikipedia.org/wiki/Chudnovsky_algorithm)
### 2. Description
- **The Chudnovsky algorithm is a fast method for calculating the digits of π.**
- **It was published by the Chudnovsky brothers in 1989, and was used in the world record calculations of 2.7 trillion digits of π in December 2009, 5 trillion digits in August 2010, 10 trillion digits in October 2011, 12.1 trillion digits in December 2013 and 22.4 trillion digits of π in November 2016.**
- **The time complexity of the algorithm is `O(N*log(N)^3)` where N as N digits of Pi.**
### 3. TestCase (No optimizations On my old laptop)
- **N = 10, Time elapsed = 0.006s**
- **N = 100, Time elapsed = 0.019s**
- **N = 1000, Time elapsed = 0.197s**
- **N = 10000, Time elapsed = 2.599s**
- **N = 100000, Time elapsed = 40.793s**
- **N = 1000000, Time elapsed = 700.538s**
- **......**
### 4. Program implements
- **[Fast Fourier transform](https://en.wikipedia.org/wiki/Fast_Fourier_transform)**
- **[Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method)**
- **[Binary_splitting method](https://en.wikipedia.org/wiki/Binary_splitting)**
### 5. Editorial:
- **[FFT based multiplication of large numbers](http://numbers.computation.free.fr/Constants/Algorithms/fft.html)**
- **[Binary splitting method](http://numbers.computation.free.fr/Constants/Algorithms/splitting.html#Brent76)**
- **[Newton's method and high order iterations](http://numbers.computation.free.fr/Constants/Algorithms/newton.html)**