fuchsia / third_party / rust-mirrors / rand / refs/heads/upstream/bit_counter / . / examples / monte-carlo.rs

// Copyright 2018 Developers of the Rand project. | |

// Copyright 2013-2018 The Rust Project Developers. | |

// | |

// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or | |

// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license | |

// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your | |

// option. This file may not be copied, modified, or distributed | |

// except according to those terms. | |

//! # Monte Carlo estimation of π | |

//! | |

//! Imagine that we have a square with sides of length 2 and a unit circle | |

//! (radius = 1), both centered at the origin. The areas are: | |

//! | |

//! ```text | |

//! area of circle = πr² = π * r * r = π | |

//! area of square = 2² = 4 | |

//! ``` | |

//! | |

//! The circle is entirely within the square, so if we sample many points | |

//! randomly from the square, roughly π / 4 of them should be inside the circle. | |

//! | |

//! We can use the above fact to estimate the value of π: pick many points in | |

//! the square at random, calculate the fraction that fall within the circle, | |

//! and multiply this fraction by 4. | |

#![cfg(feature = "std")] | |

use rand::distributions::{Distribution, Uniform}; | |

fn main() { | |

let range = Uniform::new(-1.0f64, 1.0); | |

let mut rng = rand::thread_rng(); | |

let total = 1_000_000; | |

let mut in_circle = 0; | |

for _ in 0..total { | |

let a = range.sample(&mut rng); | |

let b = range.sample(&mut rng); | |

if a * a + b * b <= 1.0 { | |

in_circle += 1; | |

} | |

} | |

// prints something close to 3.14159... | |

println!( | |

"π is approximately {}", | |

4. * (in_circle as f64) / (total as f64) | |

); | |

} |