Implement sampling from the unit circle

src/distributions/mod.rs

@@ -101,6 +101,7 @@
 //! - Multivariate probability distributions
 //!   - [`Dirichlet`] distribution
 //!   - [`UnitSphereSurface`] distribution
+//!   - [`UnitCircle`] distribution
 //!
 //! # Examples
 //!
@@ -171,6 +172,7 @@
 //! [`Uniform::new`]: struct.Uniform.html#method.new
 //! [`Uniform::new_inclusive`]: struct.Uniform.html#method.new_inclusive
 //! [`UnitSphereSurface`]: struct.UnitSphereSurface.html
+//! [`UnitCircle`]: struct.UnitCircle.html
 //! [`WeightedIndex`]: struct.WeightedIndex.html
 
 use Rng;
@@ -181,6 +183,7 @@ pub use self::float::{OpenClosed01, Open01};
 pub use self::bernoulli::Bernoulli;
 #[cfg(feature="alloc")] pub use self::weighted::{WeightedIndex, WeightedError};
 #[cfg(feature="std")] pub use self::unit_sphere::UnitSphereSurface;
+#[cfg(feature="std")] pub use self::unit_circle::UnitCircle;
 #[cfg(feature="std")] pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
 #[cfg(feature="std")] pub use self::normal::{Normal, LogNormal, StandardNormal};
 #[cfg(feature="std")] pub use self::exponential::{Exp, Exp1};
@@ -194,6 +197,7 @@ pub mod uniform;
 mod bernoulli;
 #[cfg(feature="alloc")] mod weighted;
 #[cfg(feature="std")] mod unit_sphere;
+#[cfg(feature="std")] mod unit_circle;
 #[cfg(feature="std")] mod gamma;
 #[cfg(feature="std")] mod normal;
 #[cfg(feature="std")] mod exponential;

src/distributions/unit_circle.rs

@@ -0,0 +1,94 @@
+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 {
+    uniform: Uniform<f64>,
+}
+
+impl UnitCircle {
+    /// Construct a new `UnitCircle` distribution.
+    #[inline]
+    pub fn new() -> UnitCircle {
+        UnitCircle { uniform: Uniform::new(-1., 1.) }
+    }
+}
+
+impl Distribution<[f64; 2]> for UnitCircle {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 2] {
+        let mut x1;
+        let mut x2;
+        let mut sum;
+        loop {
+            x1 = self.uniform.sample(rng);
+            x2 = self.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), [-0.8150602311723979, 0.5793762331690843]);
+        assert_eq!(dist.sample(&mut rng), [-0.056204569973983196, 0.998419273809375]);
+        assert_eq!(dist.sample(&mut rng), [0.7761923749562624, -0.630496151502733]);
+    }
+}

src/distributions/unit_sphere.rs

@@ -18,7 +18,7 @@ use distributions::{Distribution, Uniform};
 ///
 /// [^1]: Marsaglia, George (1972). [*Choosing a Point from the Surface of a
 ///       Sphere.*](https://doi.org/10.1214/aoms/1177692644)
-///       Ann. Math. Statist. 43 (1972), no. 2, 645--646.
+///       Ann. Math. Statist. 43, no. 2, 645--646.
 #[derive(Clone, Copy, Debug)]
 pub struct UnitSphereSurface {
     uniform: Uniform<f64>,