https://github.com/sysprog21/compute-pi

Leibniz formula for π
https://github.com/sysprog21/compute-pi

Last synced: 8 months ago
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Leibniz formula for π

• Host: GitHub
• URL: https://github.com/sysprog21/compute-pi
• Owner: sysprog21
• License: other
• Created: 2016-09-23T17:14:56.000Z (over 9 years ago)
• Default Branch: master
• Last Pushed: 2019-10-02T18:30:56.000Z (about 6 years ago)
• Last Synced: 2025-05-08T23:54:04.057Z (8 months ago)
• Language: C
• Size: 19.5 KB
• Stars: 11
• Watchers: 4
• Forks: 106
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# 採用離散積分的方法求圓周率，並著手透過 SIMD 指令作效能最佳化

Authored by Lee Chao Yuan ``

![](https://raw.githubusercontent.com/charles620016/embedded-fall2015/master/hw1-computePi/screenshot/integral.png)

## 相關連結

* [開發紀錄與效能分析](https://charles620016.hackpad.com/Charles-Week-1-kBMD0GhbC7d)

* [Leibniz formula for π](https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80)

## Baseline 版本

```c

double computePi_v1(size_t N)

{

    double pi = 0.0;

    double dt = 1.0 / N;                // dt = (b-a)/N, b = 1, a = 0

    for (size_t i = 0; i < N; i++) {

        double x = (double) i / N;      // x = ti = a+(b-a)*i/N = i/N

        pi += dt / (1.0 + x * x);       // integrate 1/(1+x^2), i = 0....N

    }

    return pi * 4.0;

}

```

## Benchmarking

![](https://raw.githubusercontent.com/charles620016/embedded-fall2015/master/hw1-computePi/screenshot/time_command.png)

![](https://raw.githubusercontent.com/charles620016/embedded-fall2015/master/hw1-computePi/screenshot/Wall-clock_time.png)

![](https://raw.githubusercontent.com/charles620016/embedded-fall2015/master/hw1-computePi/screenshot/CPU_time.png)