| // 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)); |
| } |