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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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