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// Copyright 2018 Developers of the Rand project.
//
// 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.
use Rng;
use distributions::{Distribution, Uniform};
/// Samples uniformly from the edge of the unit circle in two dimensions.
///
/// Implemented via a method by von Neumann[^1].
///
///
/// # Example
///
/// ```
/// use rand::distributions::{UnitCircle, Distribution};
///
/// let circle = UnitCircle::new();
/// let v = circle.sample(&mut rand::thread_rng());
/// println!("{:?} is from the unit circle.", v)
/// ```
///
/// [^1]: von Neumann, J. (1951) [*Various Techniques Used in Connection with
/// Random Digits.*](https://mcnp.lanl.gov/pdf_files/nbs_vonneumann.pdf)
/// NBS Appl. Math. Ser., No. 12. Washington, DC: U.S. Government Printing
/// Office, pp. 36-38.
#[derive(Clone, Copy, Debug)]
pub struct UnitCircle;
impl UnitCircle {
/// Construct a new `UnitCircle` distribution.
#[inline]
pub fn new() -> UnitCircle {
UnitCircle
}
}
impl Distribution<[f64; 2]> for UnitCircle {
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 2] {
let uniform = Uniform::new(-1., 1.);
let mut x1;
let mut x2;
let mut sum;
loop {
x1 = uniform.sample(rng);
x2 = uniform.sample(rng);
sum = x1*x1 + x2*x2;
if sum < 1. {
break;
}
}
let diff = x1*x1 - x2*x2;
[diff / sum, 2.*x1*x2 / sum]
}
}
#[cfg(test)]
mod tests {
use distributions::Distribution;
use super::UnitCircle;
/// Assert that two numbers are almost equal to each other.
///
/// On panic, this macro will print the values of the expressions with their
/// debug representations.
macro_rules! assert_almost_eq {
($a:expr, $b:expr, $prec:expr) => (
let diff = ($a - $b).abs();
if diff > $prec {
panic!(format!(
"assertion failed: `abs(left - right) = {:.1e} < {:e}`, \
(left: `{}`, right: `{}`)",
diff, $prec, $a, $b));
}
);
}
#[test]
fn norm() {
let mut rng = ::test::rng(1);
let dist = UnitCircle::new();
for _ in 0..1000 {
let x = dist.sample(&mut rng);
assert_almost_eq!(x[0]*x[0] + x[1]*x[1], 1., 1e-15);
}
}
#[test]
fn value_stability() {
let mut rng = ::test::rng(2);
let dist = UnitCircle::new();
assert_eq!(dist.sample(&mut rng), [-0.8032118336637037, 0.5956935036263119]);
assert_eq!(dist.sample(&mut rng), [-0.4742919588505423, -0.880367615130018]);
assert_eq!(dist.sample(&mut rng), [0.9297328981467168, 0.368234623716601]);
}
}
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