vendor/rand-0.5.6/examples/monte-carlo.rs

   1 // Copyright 2013-2018 The Rust Project Developers. See the COPYRIGHT
   2 // file at the top-level directory of this distribution and at
   3 // https://rust-lang.org/COPYRIGHT.
   4 //
   5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
   6 // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
   7 // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
   8 // option. This file may not be copied, modified, or distributed
   9 // except according to those terms.
  10
  11 //! # Monte Carlo estimation of π
  12 //!
  13 //! Imagine that we have a square with sides of length 2 and a unit circle
  14 //! (radius = 1), both centered at the origin. The areas are:
  15 //!
  16 //! ```text
  17 //!     area of circle  = πr² = π * r * r = π
  18 //!     area of square  = 2² = 4
  19 //! ```
  20 //!
  21 //! The circle is entirely within the square, so if we sample many points
  22 //! randomly from the square, roughly π / 4 of them should be inside the circle.
  23 //!
  24 //! We can use the above fact to estimate the value of π: pick many points in
  25 //! the square at random, calculate the fraction that fall within the circle,
  26 //! and multiply this fraction by 4.
  27
  28 #![cfg(feature="std")]
  29
  30
  31 extern crate rand;
  32
  33 use rand::distributions::{Distribution, Uniform};
  34
  35 fn main() {
  36    let range = Uniform::new(-1.0f64, 1.0);
  37    let mut rng = rand::thread_rng();
  38
  39    let total = 1_000_000;
  40    let mut in_circle = 0;
  41
  42    for _ in 0..total {
  43        let a = range.sample(&mut rng);
  44        let b = range.sample(&mut rng);
  45        if a*a + b*b <= 1.0 {
  46            in_circle += 1;
  47        }
  48    }
  49
  50    // prints something close to 3.14159...
  51    println!("π is approximately {}", 4. * (in_circle as f64) / (total as f64));
  52 }