1 // Copyright 2018 Developers of the Rand project.
2 // Copyright 2013 The Rust Project Developers.
3 //
4 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
5 // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
6 // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
7 // option. This file may not be copied, modified, or distributed
8 // except according to those terms.
9 
10 //! The exponential distribution.
11 
12 use {Rng};
13 use distributions::{ziggurat_tables, Distribution};
14 use distributions::utils::ziggurat;
15 
16 /// Samples floating-point numbers according to the exponential distribution,
17 /// with rate parameter `λ = 1`. This is equivalent to `Exp::new(1.0)` or
18 /// sampling with `-rng.gen::<f64>().ln()`, but faster.
19 ///
20 /// See `Exp` for the general exponential distribution.
21 ///
22 /// Implemented via the ZIGNOR variant[^1] of the Ziggurat method. The exact
23 /// description in the paper was adjusted to use tables for the exponential
24 /// distribution rather than normal.
25 ///
26 /// [^1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
27 ///       Generate Normal Random Samples*](
28 ///       https://www.doornik.com/research/ziggurat.pdf).
29 ///       Nuffield College, Oxford
30 ///
31 /// # Example
32 /// ```
33 /// use rand::prelude::*;
34 /// use rand::distributions::Exp1;
35 ///
36 /// let val: f64 = SmallRng::from_entropy().sample(Exp1);
37 /// println!("{}", val);
38 /// ```
39 #[derive(Clone, Copy, Debug)]
40 pub struct Exp1;
41 
42 // This could be done via `-rng.gen::<f64>().ln()` but that is slower.
43 impl Distribution<f64> for Exp1 {
44     #[inline]
sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f6445     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
46         #[inline]
47         fn pdf(x: f64) -> f64 {
48             (-x).exp()
49         }
50         #[inline]
51         fn zero_case<R: Rng + ?Sized>(rng: &mut R, _u: f64) -> f64 {
52             ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln()
53         }
54 
55         ziggurat(rng, false,
56                  &ziggurat_tables::ZIG_EXP_X,
57                  &ziggurat_tables::ZIG_EXP_F,
58                  pdf, zero_case)
59     }
60 }
61 
62 /// The exponential distribution `Exp(lambda)`.
63 ///
64 /// This distribution has density function: `f(x) = lambda * exp(-lambda * x)`
65 /// for `x > 0`.
66 ///
67 /// Note that [`Exp1`][crate::distributions::Exp1] is an optimised implementation for `lambda = 1`.
68 ///
69 /// # Example
70 ///
71 /// ```
72 /// use rand::distributions::{Exp, Distribution};
73 ///
74 /// let exp = Exp::new(2.0);
75 /// let v = exp.sample(&mut rand::thread_rng());
76 /// println!("{} is from a Exp(2) distribution", v);
77 /// ```
78 #[derive(Clone, Copy, Debug)]
79 pub struct Exp {
80     /// `lambda` stored as `1/lambda`, since this is what we scale by.
81     lambda_inverse: f64
82 }
83 
84 impl Exp {
85     /// Construct a new `Exp` with the given shape parameter
86     /// `lambda`. Panics if `lambda <= 0`.
87     #[inline]
new(lambda: f64) -> Exp88     pub fn new(lambda: f64) -> Exp {
89         assert!(lambda > 0.0, "Exp::new called with `lambda` <= 0");
90         Exp { lambda_inverse: 1.0 / lambda }
91     }
92 }
93 
94 impl Distribution<f64> for Exp {
sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f6495     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
96         let n: f64 = rng.sample(Exp1);
97         n * self.lambda_inverse
98     }
99 }
100 
101 #[cfg(test)]
102 mod test {
103     use distributions::Distribution;
104     use super::Exp;
105 
106     #[test]
test_exp()107     fn test_exp() {
108         let exp = Exp::new(10.0);
109         let mut rng = ::test::rng(221);
110         for _ in 0..1000 {
111             assert!(exp.sample(&mut rng) >= 0.0);
112         }
113     }
114     #[test]
115     #[should_panic]
test_exp_invalid_lambda_zero()116     fn test_exp_invalid_lambda_zero() {
117         Exp::new(0.0);
118     }
119     #[test]
120     #[should_panic]
test_exp_invalid_lambda_neg()121     fn test_exp_invalid_lambda_neg() {
122         Exp::new(-10.0);
123     }
124 }
125