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// Copyright 2018 Developers of the Rand project.
// Copyright 2013 The Rust Project Developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! The exponential distribution.
use crate::utils::ziggurat;
use num_traits::Float;
use crate::{ziggurat_tables, Distribution};
use rand::Rng;
use core::fmt;
/// 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*](
/// Nuffield College, Oxford
///
/// # Example
/// ```
/// use rand::prelude::*;
/// use rand_distr::Exp1;
///
/// let val: f64 = thread_rng().sample(Exp1);
/// println!("{}", val);
/// ```
#[derive(Clone, Copy, Debug)]
#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
pub struct Exp1;
impl Distribution<f32> for Exp1 {
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f32 {
// TODO: use optimal 32-bit implementation
let x: f64 = self.sample(rng);
x as f32
}
}
// 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`, when `lambda > 0`. For `lambda = 0`, all samples yield infinity.
///
/// Note that [`Exp1`](crate::Exp1) is an optimised implementation for `lambda = 1`.
///
/// # Example
///
/// ```
/// use rand_distr::{Exp, Distribution};
///
/// let exp = Exp::new(2.0).unwrap();
/// let v = exp.sample(&mut rand::thread_rng());
/// println!("{} is from a Exp(2) distribution", v);
/// ```
#[derive(Clone, Copy, Debug)]
#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
pub struct Exp<F>
where F: Float, Exp1: Distribution<F>
{
/// `lambda` stored as `1/lambda`, since this is what we scale by.
lambda_inverse: F,
}
/// Error type returned from `Exp::new`.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `lambda < 0` or `nan`.
LambdaTooSmall,
}
impl fmt::Display for Error {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.write_str(match self {
Error::LambdaTooSmall => "lambda is negative or NaN in exponential distribution",
})
}
}
#[cfg(feature = "std")]
#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
impl std::error::Error for Error {}
impl<F: Float> Exp<F>
where F: Float, Exp1: Distribution<F>
{
/// Construct a new `Exp` with the given shape parameter
/// `lambda`.
///
/// # Remarks
///
/// For custom types `N` implementing the [`Float`] trait,
/// the case `lambda = 0` is handled as follows: each sample corresponds
/// to a sample from an `Exp1` multiplied by `1 / 0`. Primitive types
/// yield infinity, since `1 / 0 = infinity`.
#[inline]
pub fn new(lambda: F) -> Result<Exp<F>, Error> {
if !(lambda >= F::zero()) {
return Err(Error::LambdaTooSmall);
}
Ok(Exp {
lambda_inverse: F::one() / lambda,
})
}
}
impl<F> Distribution<F> for Exp<F>
where F: Float, Exp1: Distribution<F>
{
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
rng.sample(Exp1) * self.lambda_inverse
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn test_exp() {
let exp = Exp::new(10.0).unwrap();
let mut rng = crate::test::rng(221);
for _ in 0..1000 {
assert!(exp.sample(&mut rng) >= 0.0);
}
}
#[test]
fn test_zero() {
let d = Exp::new(0.0).unwrap();
assert_eq!(d.sample(&mut crate::test::rng(21)), f64::infinity());
}
#[test]
#[should_panic]
fn test_exp_invalid_lambda_neg() {
Exp::new(-10.0).unwrap();
}
#[test]
#[should_panic]
fn test_exp_invalid_lambda_nan() {
Exp::new(f64::nan()).unwrap();
}
}