      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
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124

    // Copyright 2018 Developers of the Rand project.
    // Copyright 2013 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.

    //! The exponential distribution.

    use {Rng};
    use distributions::{ziggurat_tables, Distribution};
    use distributions::utils::ziggurat;

    /// Samples floating-point numbers according to the exponential distribution,
    /// with rate parameter `λ = 1`. This is equivalent to `Exp::new(1.0)` or
    /// sampling with `-rng.gen::<f64>().ln()`, but faster.
    ///
    /// See `Exp` for the general exponential distribution.
    ///
    /// Implemented via the ZIGNOR variant[^1] of the Ziggurat method. The exact
    /// description in the paper was adjusted to use tables for the exponential
    /// distribution rather than normal.
    ///
    /// [^1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
    ///       Generate Normal Random Samples*](
    ///       https://www.doornik.com/research/ziggurat.pdf).
    ///       Nuffield College, Oxford
    ///
    /// # Example
    /// ```
    /// use rand::prelude::*;
    /// use rand::distributions::Exp1;
    ///
    /// let val: f64 = SmallRng::from_entropy().sample(Exp1);
    /// println!("{}", val);
    /// ```
    #[derive(Clone, Copy, Debug)]
    pub struct Exp1;

    // This could be done via `-rng.gen::<f64>().ln()` but that is slower.
    impl Distribution<f64> for Exp1 {
        #[inline]
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
            #[inline]
            fn pdf(x: f64) -> f64 {
                (-x).exp()
            }
            #[inline]
            fn zero_case<R: Rng + ?Sized>(rng: &mut R, _u: f64) -> f64 {
                ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln()
            }

            ziggurat(rng, false,
                     &ziggurat_tables::ZIG_EXP_X,
                     &ziggurat_tables::ZIG_EXP_F,
                     pdf, zero_case)
        }
    }

    /// The exponential distribution `Exp(lambda)`.
    ///
    /// This distribution has density function: `f(x) = lambda * exp(-lambda * x)`
    /// for `x > 0`.
    ///
    /// Note that [`Exp1`][crate::distributions::Exp1] is an optimised implementation for `lambda = 1`.
    ///
    /// # Example
    ///
    /// ```
    /// use rand::distributions::{Exp, Distribution};
    ///
    /// let exp = Exp::new(2.0);
    /// let v = exp.sample(&mut rand::thread_rng());
    /// println!("{} is from a Exp(2) distribution", v);
    /// ```
    #[derive(Clone, Copy, Debug)]
    pub struct Exp {
        /// `lambda` stored as `1/lambda`, since this is what we scale by.
        lambda_inverse: f64
    }

    impl Exp {
        /// Construct a new `Exp` with the given shape parameter
        /// `lambda`. Panics if `lambda <= 0`.
        #[inline]
        pub fn new(lambda: f64) -> Exp {
            assert!(lambda > 0.0, "Exp::new called with `lambda` <= 0");
            Exp { lambda_inverse: 1.0 / lambda }
        }
    }

    impl Distribution<f64> for Exp {
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
            let n: f64 = rng.sample(Exp1);
            n * self.lambda_inverse
        }
    }

    #[cfg(test)]
    mod test {
        use distributions::Distribution;
        use super::Exp;

        #[test]
        fn test_exp() {
            let exp = Exp::new(10.0);
            let mut rng = ::test::rng(221);
            for _ in 0..1000 {
                assert!(exp.sample(&mut rng) >= 0.0);
            }
        }
        #[test]
        #[should_panic]
        fn test_exp_invalid_lambda_zero() {
            Exp::new(0.0);
        }
        #[test]
        #[should_panic]
        fn test_exp_invalid_lambda_neg() {
            Exp::new(-10.0);
        }
    }

# 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`)