| // 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")] |

| |

| |

| extern crate rand; |

| |

| 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)); |

| } |