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    // Copyright 2018 Developers of the Rand project.
    // Copyright 2013-2017 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.

    //! Generating random samples from probability distributions
    //!
    //! This module is the home of the [`Distribution`] trait and several of its
    //! implementations. It is the workhorse behind some of the convenient
    //! functionality of the [`Rng`] trait, e.g. [`Rng::gen`], [`Rng::gen_range`] and
    //! of course [`Rng::sample`].
    //!
    //! Abstractly, a [probability distribution] describes the probability of
    //! occurance of each value in its sample space.
    //!
    //! More concretely, an implementation of `Distribution<T>` for type `X` is an
    //! algorithm for choosing values from the sample space (a subset of `T`)
    //! according to the distribution `X` represents, using an external source of
    //! randomness (an RNG supplied to the `sample` function).
    //!
    //! A type `X` may implement `Distribution<T>` for multiple types `T`.
    //! Any type implementing [`Distribution`] is stateless (i.e. immutable),
    //! but it may have internal parameters set at construction time (for example,
    //! [`Uniform`] allows specification of its sample space as a range within `T`).
    //!
    //!
    //! # The `Standard` distribution
    //!
    //! The [`Standard`] distribution is important to mention. This is the
    //! distribution used by [`Rng::gen()`] and represents the "default" way to
    //! produce a random value for many different types, including most primitive
    //! types, tuples, arrays, and a few derived types. See the documentation of
    //! [`Standard`] for more details.
    //!
    //! Implementing `Distribution<T>` for [`Standard`] for user types `T` makes it
    //! possible to generate type `T` with [`Rng::gen()`], and by extension also
    //! with the [`random()`] function.
    //!
    //! ## Random characters
    //!
    //! [`Alphanumeric`] is a simple distribution to sample random letters and
    //! numbers of the `char` type; in contrast [`Standard`] may sample any valid
    //! `char`.
    //!
    //!
    //! # Uniform numeric ranges
    //!
    //! The [`Uniform`] distribution is more flexible than [`Standard`], but also
    //! more specialised: it supports fewer target types, but allows the sample
    //! space to be specified as an arbitrary range within its target type `T`.
    //! Both [`Standard`] and [`Uniform`] are in some sense uniform distributions.
    //!
    //! Values may be sampled from this distribution using [`Rng::gen_range`] or
    //! by creating a distribution object with [`Uniform::new`],
    //! [`Uniform::new_inclusive`] or `From<Range>`. When the range limits are not
    //! known at compile time it is typically faster to reuse an existing
    //! distribution object than to call [`Rng::gen_range`].
    //!
    //! User types `T` may also implement `Distribution<T>` for [`Uniform`],
    //! although this is less straightforward than for [`Standard`] (see the
    //! documentation in the [`uniform`] module. Doing so enables generation of
    //! values of type `T` with  [`Rng::gen_range`].
    //!
    //! ## Open and half-open ranges
    //!
    //! There are surprisingly many ways to uniformly generate random floats. A
    //! range between 0 and 1 is standard, but the exact bounds (open vs closed)
    //! and accuracy differ. In addition to the [`Standard`] distribution Rand offers
    //! [`Open01`] and [`OpenClosed01`]. See "Floating point implementation" section of
    //! [`Standard`] documentation for more details.
    //!
    //! # Non-uniform sampling
    //!
    //! Sampling a simple true/false outcome with a given probability has a name:
    //! the [`Bernoulli`] distribution (this is used by [`Rng::gen_bool`]).
    //!
    //! For weighted sampling from a sequence of discrete values, use the
    //! [`weighted`] module.
    //!
    //! This crate no longer includes other non-uniform distributions; instead
    //! it is recommended that you use either [`rand_distr`] or [`statrs`].
    //!
    //!
    //! [probability distribution]: https://en.wikipedia.org/wiki/Probability_distribution
    //! [`rand_distr`]: https://crates.io/crates/rand_distr
    //! [`statrs`]: https://crates.io/crates/statrs

    //! [`Alphanumeric`]: distributions::Alphanumeric
    //! [`Bernoulli`]: distributions::Bernoulli
    //! [`Open01`]: distributions::Open01
    //! [`OpenClosed01`]: distributions::OpenClosed01
    //! [`Standard`]: distributions::Standard
    //! [`Uniform`]: distributions::Uniform
    //! [`Uniform::new`]: distributions::Uniform::new
    //! [`Uniform::new_inclusive`]: distributions::Uniform::new_inclusive
    //! [`weighted`]: distributions::weighted
    //! [`rand_distr`]: https://crates.io/crates/rand_distr
    //! [`statrs`]: https://crates.io/crates/statrs

    use core::iter;
    use crate::Rng;

    pub use self::other::Alphanumeric;
    #[doc(inline)] pub use self::uniform::Uniform;
    pub use self::float::{OpenClosed01, Open01};
    pub use self::bernoulli::{Bernoulli, BernoulliError};
    #[cfg(feature="alloc")] pub use self::weighted::{WeightedIndex, WeightedError};

    // The following are all deprecated after being moved to rand_distr
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::unit_sphere::UnitSphereSurface;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::unit_circle::UnitCircle;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::gamma::{Gamma, ChiSquared, FisherF,
        StudentT, Beta};
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::normal::{Normal, LogNormal, StandardNormal};
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::exponential::{Exp, Exp1};
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::pareto::Pareto;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::poisson::Poisson;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::binomial::Binomial;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::cauchy::Cauchy;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::dirichlet::Dirichlet;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::triangular::Triangular;
    #[allow(deprecated)]
    #[cfg(feature="std")] pub use self::weibull::Weibull;

    pub mod uniform;
    mod bernoulli;
    #[cfg(feature="alloc")] pub mod weighted;
    #[cfg(feature="std")] mod unit_sphere;
    #[cfg(feature="std")] mod unit_circle;
    #[cfg(feature="std")] mod gamma;
    #[cfg(feature="std")] mod normal;
    #[cfg(feature="std")] mod exponential;
    #[cfg(feature="std")] mod pareto;
    #[cfg(feature="std")] mod poisson;
    #[cfg(feature="std")] mod binomial;
    #[cfg(feature="std")] mod cauchy;
    #[cfg(feature="std")] mod dirichlet;
    #[cfg(feature="std")] mod triangular;
    #[cfg(feature="std")] mod weibull;

    mod float;
    #[doc(hidden)] pub mod hidden_export {
        pub use super::float::IntoFloat;   // used by rand_distr
    }
    mod integer;
    mod other;
    mod utils;
    #[cfg(feature="std")] mod ziggurat_tables;

    /// Types (distributions) that can be used to create a random instance of `T`.
    ///
    /// It is possible to sample from a distribution through both the
    /// `Distribution` and [`Rng`] traits, via `distr.sample(&mut rng)` and
    /// `rng.sample(distr)`. They also both offer the [`sample_iter`] method, which
    /// produces an iterator that samples from the distribution.
    ///
    /// All implementations are expected to be immutable; this has the significant
    /// advantage of not needing to consider thread safety, and for most
    /// distributions efficient state-less sampling algorithms are available.
    ///
    /// [`sample_iter`]: Distribution::method.sample_iter
    pub trait Distribution<T> {
        /// Generate a random value of `T`, using `rng` as the source of randomness.
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> T;

        /// Create an iterator that generates random values of `T`, using `rng` as
        /// the source of randomness.
        ///
        /// Note that this function takes `self` by value. This works since
        /// `Distribution<T>` is impl'd for `&D` where `D: Distribution<T>`,
        /// however borrowing is not automatic hence `distr.sample_iter(...)` may
        /// need to be replaced with `(&distr).sample_iter(...)` to borrow or
        /// `(&*distr).sample_iter(...)` to reborrow an existing reference.
        ///
        /// # Example
        ///
        /// ```
        /// use rand::thread_rng;
        /// use rand::distributions::{Distribution, Alphanumeric, Uniform, Standard};
        ///
        /// let rng = thread_rng();
        ///
        /// // Vec of 16 x f32:
        /// let v: Vec<f32> = Standard.sample_iter(rng).take(16).collect();
        ///
        /// // String:
        /// let s: String = Alphanumeric.sample_iter(rng).take(7).collect();
        ///
        /// // Dice-rolling:
        /// let die_range = Uniform::new_inclusive(1, 6);
        /// let mut roll_die = die_range.sample_iter(rng);
        /// while roll_die.next().unwrap() != 6 {
        ///     println!("Not a 6; rolling again!");
        /// }
        /// ```
        fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>
        where R: Rng, Self: Sized
        {
            DistIter {
                distr: self,
                rng: rng,
                phantom: ::core::marker::PhantomData,
            }
        }
    }

    impl<'a, T, D: Distribution<T>> Distribution<T> for &'a D {
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> T {
            (*self).sample(rng)
        }
    }

    /// An iterator that generates random values of `T` with distribution `D`,
    /// using `R` as the source of randomness.
    ///
    /// This `struct` is created by the [`sample_iter`] method on [`Distribution`].
    /// See its documentation for more.
    ///
    /// [`sample_iter`]: Distribution::sample_iter
    #[derive(Debug)]
    pub struct DistIter<D, R, T> {
        distr: D,
        rng: R,
        phantom: ::core::marker::PhantomData<T>,
    }

    impl<D, R, T> Iterator for DistIter<D, R, T>
        where D: Distribution<T>, R: Rng
    {
        type Item = T;

        #[inline(always)]
        fn next(&mut self) -> Option<T> {
            // Here, self.rng may be a reference, but we must take &mut anyway.
            // Even if sample could take an R: Rng by value, we would need to do this
            // since Rng is not copyable and we cannot enforce that this is "reborrowable".
            Some(self.distr.sample(&mut self.rng))
        }

        fn size_hint(&self) -> (usize, Option<usize>) {
            (usize::max_value(), None)
        }
    }

    impl<D, R, T> iter::FusedIterator for DistIter<D, R, T>
        where D: Distribution<T>, R: Rng {}

    #[cfg(features = "nightly")]
    impl<D, R, T> iter::TrustedLen for DistIter<D, R, T>
        where D: Distribution<T>, R: Rng {}

    /// A generic random value distribution, implemented for many primitive types.
    /// Usually generates values with a numerically uniform distribution, and with a
    /// range appropriate to the type.
    ///
    /// ## Provided implementations
    ///
    /// Assuming the provided `Rng` is well-behaved, these implementations
    /// generate values with the following ranges and distributions:
    ///
    /// * Integers (`i32`, `u32`, `isize`, `usize`, etc.): Uniformly distributed
    ///   over all values of the type.
    /// * `char`: Uniformly distributed over all Unicode scalar values, i.e. all
    ///   code points in the range `0...0x10_FFFF`, except for the range
    ///   `0xD800...0xDFFF` (the surrogate code points). This includes
    ///   unassigned/reserved code points.
    /// * `bool`: Generates `false` or `true`, each with probability 0.5.
    /// * Floating point types (`f32` and `f64`): Uniformly distributed in the
    ///   half-open range `[0, 1)`. See notes below.
    /// * Wrapping integers (`Wrapping<T>`), besides the type identical to their
    ///   normal integer variants.
    ///
    /// The `Standard` distribution also supports generation of the following
    /// compound types where all component types are supported:
    ///
    /// *   Tuples (up to 12 elements): each element is generated sequentially.
    /// *   Arrays (up to 32 elements): each element is generated sequentially;
    ///     see also [`Rng::fill`] which supports arbitrary array length for integer
    ///     types and tends to be faster for `u32` and smaller types.
    /// *   `Option<T>` first generates a `bool`, and if true generates and returns
    ///     `Some(value)` where `value: T`, otherwise returning `None`.
    ///
    /// ## Custom implementations
    ///
    /// The [`Standard`] distribution may be implemented for user types as follows:
    ///
    /// ```
    /// # #![allow(dead_code)]
    /// use rand::Rng;
    /// use rand::distributions::{Distribution, Standard};
    ///
    /// struct MyF32 {
    ///     x: f32,
    /// }
    ///
    /// impl Distribution<MyF32> for Standard {
    ///     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> MyF32 {
    ///         MyF32 { x: rng.gen() }
    ///     }
    /// }
    /// ```
    ///
    /// ## Example usage
    /// ```
    /// use rand::prelude::*;
    /// use rand::distributions::Standard;
    ///
    /// let val: f32 = StdRng::from_entropy().sample(Standard);
    /// println!("f32 from [0, 1): {}", val);
    /// ```
    ///
    /// # Floating point implementation
    /// The floating point implementations for `Standard` generate a random value in
    /// the half-open interval `[0, 1)`, i.e. including 0 but not 1.
    ///
    /// All values that can be generated are of the form `n * ε/2`. For `f32`
    /// the 23 most significant random bits of a `u32` are used and for `f64` the
    /// 53 most significant bits of a `u64` are used. The conversion uses the
    /// multiplicative method: `(rng.gen::<$uty>() >> N) as $ty * (ε/2)`.
    ///
    /// See also: [`Open01`] which samples from `(0, 1)`, [`OpenClosed01`] which
    /// samples from `(0, 1]` and `Rng::gen_range(0, 1)` which also samples from
    /// `[0, 1)`. Note that `Open01` and `gen_range` (which uses [`Uniform`]) use
    /// transmute-based methods which yield 1 bit less precision but may perform
    /// faster on some architectures (on modern Intel CPUs all methods have
    /// approximately equal performance).
    ///
    /// [`Uniform`]: uniform::Uniform
    #[derive(Clone, Copy, Debug)]
    pub struct Standard;

    #[cfg(all(test, feature = "std"))]
    mod tests {
        use crate::Rng;
        use super::{Distribution, Uniform};

        #[test]
        fn test_distributions_iter() {
            use crate::distributions::Open01;
            let mut rng = crate::test::rng(210);
            let distr = Open01;
            let results: Vec<f32> = distr.sample_iter(&mut rng).take(100).collect();
            println!("{:?}", results);
        }

        #[test]
        fn test_make_an_iter() {
            fn ten_dice_rolls_other_than_five<'a, R: Rng>(rng: &'a mut R) -> impl Iterator<Item = i32> + 'a {
                Uniform::new_inclusive(1, 6)
                    .sample_iter(rng)
                    .filter(|x| *x != 5)
                    .take(10)
            }

            let mut rng = crate::test::rng(211);
            let mut count = 0;
            for val in ten_dice_rolls_other_than_five(&mut rng) {
                assert!(val >= 1 && val <= 6 && val != 5);
                count += 1;
            }
            assert_eq!(count, 10);
        }
    }

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