      1
      2
      3
      4
      5
      6
      7
      8
      9
     10
     11
     12
     13
     14
     15
     16
     17
     18
     19
     20
     21
     22
     23
     24
     25
     26
     27
     28
     29
     30
     31
     32
     33
     34
     35
     36
     37
     38
     39
     40
     41
     42
     43
     44
     45
     46
     47
     48
     49
     50
     51
     52
     53
     54
     55
     56
     57
     58
     59
     60
     61
     62
     63
     64
     65
     66
     67
     68
     69
     70
     71
     72
     73
     74
     75
     76
     77
     78
     79
     80
     81
     82
     83
     84
     85
     86
     87
     88
     89
     90
     91
     92
     93
     94
     95
     96
     97
     98
     99
    100

    // 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.

    #![allow(deprecated)]

    use crate::Rng;
    use crate::distributions::{Distribution, Uniform};

    /// Samples uniformly from the edge of the unit circle in two dimensions.
    ///
    /// Implemented via a method by von Neumann[^1].
    ///
    /// [^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.
    #[deprecated(since="0.7.0", note="moved to rand_distr crate")]
    #[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 crate::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 = crate::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 = crate::test::rng(2);
            let expected = [
                    [-0.9965658683520504, -0.08280380447614634],
                    [-0.9790853270389644, -0.20345004884984505],
                    [-0.8449189758898707, 0.5348943112253227],
                ];
            let samples = [
                    UnitCircle.sample(&mut rng),
                    UnitCircle.sample(&mut rng),
                    UnitCircle.sample(&mut rng),
                ];
            assert_eq!(samples, expected);
        }
    }

# Help

## Keyboard Shortcuts

`?`
  Show this help dialog
`S`
  Focus the search field
`↑`
  Move up in search results
`↓`
  Move down in search results
`↹`
  Switch tab
`⏎`
  Go to active search result
`+`
  Expand all sections
`-`
  Collapse all sections

## Search Tricks

Prefix searches with a type followed by a colon (e.g., `fn:`) to restrict the search to a given type.

Accepted types are: `fn`, `mod`, `struct`, `enum`, `trait`, `type`, `macro`, and `const`.

Search functions by type signature (e.g., `vec -> usize` or `* -> vec`)

Search multiple things at once by splitting your query with comma (e.g., `str,u8` or `String,struct:Vec,test`)