vendor/rand/examples/monte-carlo.rs

   1 // Copyright 2018 Developers of the Rand project.
   2 // Copyright 2013-2018 The Rust Project Developers.
   3 //
   4 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
   5 // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
   6 // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
   7 // option. This file may not be copied, modified, or distributed
   8 // except according to those terms.
   9
  10 //! # Monte Carlo estimation of π
  11 //!
  12 //! Imagine that we have a square with sides of length 2 and a unit circle
  13 //! (radius = 1), both centered at the origin. The areas are:
  14 //!
  15 //! ```text
  16 //!     area of circle  = πr² = π * r * r = π
  17 //!     area of square  = 2² = 4
  18 //! ```
  19 //!
  20 //! The circle is entirely within the square, so if we sample many points
  21 //! randomly from the square, roughly π / 4 of them should be inside the circle.
  22 //!
  23 //! We can use the above fact to estimate the value of π: pick many points in
  24 //! the square at random, calculate the fraction that fall within the circle,
  25 //! and multiply this fraction by 4.
  26
  27 #![cfg(feature = "std")]
  28
  29 use rand::distributions::{Distribution, Uniform};
  30
  31 fn main() {
  32     let range = Uniform::new(-1.0f64, 1.0);
  33     let mut rng = rand::thread_rng();
  34
  35     let total = 1_000_000;
  36     let mut in_circle = 0;
  37
  38     for _ in 0..total {
  39         let a = range.sample(&mut rng);
  40         let b = range.sample(&mut rng);
  41         if a*a + b*b <= 1.0 {
  42             in_circle += 1;
  43         }
  44     }
  45
  46     // prints something close to 3.14159...
  47     println!("π is approximately {}", 4. * (in_circle as f64) / (total as f64));
  48 }