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    // Copyright 2013 The Rust Project Developers. See the COPYRIGHT
    // file at the top-level directory of this distribution and at
    // http://rust-lang.org/COPYRIGHT.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! Sampling from random distributions.
    //!
    //! This is a generalization of `Rand` to allow parameters to control the
    //! exact properties of the generated values, e.g. the mean and standard
    //! deviation of a normal distribution. The `Sample` trait is the most
    //! general, and allows for generating values that change some state
    //! internally. The `IndependentSample` trait is for generating values
    //! that do not need to record state.

    use std::marker;

    use {Rng, Rand};

    pub use self::range::Range;
    pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
    pub use self::normal::{Normal, LogNormal};
    pub use self::exponential::Exp;

    pub mod range;
    pub mod gamma;
    pub mod normal;
    pub mod exponential;

    /// Types that can be used to create a random instance of `Support`.
    pub trait Sample<Support> {
        /// Generate a random value of `Support`, using `rng` as the
        /// source of randomness.
        fn sample<R: Rng>(&mut self, rng: &mut R) -> Support;
    }

    /// `Sample`s that do not require keeping track of state.
    ///
    /// Since no state is recorded, each sample is (statistically)
    /// independent of all others, assuming the `Rng` used has this
    /// property.
    // FIXME maybe having this separate is overkill (the only reason is to
    // take &self rather than &mut self)? or maybe this should be the
    // trait called `Sample` and the other should be `DependentSample`.
    pub trait IndependentSample<Support>: Sample<Support> {
        /// Generate a random value.
        fn ind_sample<R: Rng>(&self, &mut R) -> Support;
    }

    /// A wrapper for generating types that implement `Rand` via the
    /// `Sample` & `IndependentSample` traits.
    pub struct RandSample<Sup> {
        _marker: marker::PhantomData<fn() -> Sup>,
    }

    impl<Sup> Copy for RandSample<Sup> {}
    impl<Sup> Clone for RandSample<Sup> {
        fn clone(&self) -> Self { *self }
    }

    impl<Sup: Rand> Sample<Sup> for RandSample<Sup> {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup { self.ind_sample(rng) }
    }

    impl<Sup: Rand> IndependentSample<Sup> for RandSample<Sup> {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup {
            rng.gen()
        }
    }

    impl<Sup> RandSample<Sup> {
        pub fn new() -> RandSample<Sup> {
            RandSample { _marker: marker::PhantomData }
        }
    }

    /// A value with a particular weight for use with `WeightedChoice`.
    #[derive(Copy)]
    #[derive(Clone)]
    pub struct Weighted<T> {
        /// The numerical weight of this item
        pub weight: u32,
        /// The actual item which is being weighted
        pub item: T,
    }

    /// A distribution that selects from a finite collection of weighted items.
    ///
    /// Each item has an associated weight that influences how likely it
    /// is to be chosen: higher weight is more likely.
    ///
    /// The `Clone` restriction is a limitation of the `Sample` and
    /// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for
    /// all `T`, as is `u32`, so one can store references or indices into
    /// another vector.
    ///
    /// # Example
    ///
    /// ```rust
    /// use rand::distributions::{Weighted, WeightedChoice, IndependentSample};
    ///
    /// let mut items = vec!(Weighted { weight: 2, item: 'a' },
    ///                      Weighted { weight: 4, item: 'b' },
    ///                      Weighted { weight: 1, item: 'c' });
    /// let wc = WeightedChoice::new(&mut items);
    /// let mut rng = rand::thread_rng();
    /// for _ in 0..16 {
    ///      // on average prints 'a' 4 times, 'b' 8 and 'c' twice.
    ///      println!("{}", wc.ind_sample(&mut rng));
    /// }
    /// ```
    pub struct WeightedChoice<'a, T:'a> {
        items: &'a mut [Weighted<T>],
        weight_range: Range<u32>
    }

    impl<'a, T: Clone> WeightedChoice<'a, T> {
        /// Create a new `WeightedChoice`.
        ///
        /// Panics if:
        /// - `v` is empty
        /// - the total weight is 0
        /// - the total weight is larger than a `u32` can contain.
        pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> {
            // strictly speaking, this is subsumed by the total weight == 0 case
            assert!(!items.is_empty(), "WeightedChoice::new called with no items");

            let mut running_total: u32 = 0;

            // we convert the list from individual weights to cumulative
            // weights so we can binary search. This *could* drop elements
            // with weight == 0 as an optimisation.
            for item in items.iter_mut() {
                running_total = match running_total.checked_add(item.weight) {
                    Some(n) => n,
                    None => panic!("WeightedChoice::new called with a total weight \
                                   larger than a u32 can contain")
                };

                item.weight = running_total;
            }
            assert!(running_total != 0, "WeightedChoice::new called with a total weight of 0");

            WeightedChoice {
                items: items,
                // we're likely to be generating numbers in this range
                // relatively often, so might as well cache it
                weight_range: Range::new(0, running_total)
            }
        }
    }

    impl<'a, T: Clone> Sample<T> for WeightedChoice<'a, T> {
        fn sample<R: Rng>(&mut self, rng: &mut R) -> T { self.ind_sample(rng) }
    }

    impl<'a, T: Clone> IndependentSample<T> for WeightedChoice<'a, T> {
        fn ind_sample<R: Rng>(&self, rng: &mut R) -> T {
            // we want to find the first element that has cumulative
            // weight > sample_weight, which we do by binary since the
            // cumulative weights of self.items are sorted.

            // choose a weight in [0, total_weight)
            let sample_weight = self.weight_range.ind_sample(rng);

            // short circuit when it's the first item
            if sample_weight < self.items[0].weight {
                return self.items[0].item.clone();
            }

            let mut idx = 0;
            let mut modifier = self.items.len();

            // now we know that every possibility has an element to the
            // left, so we can just search for the last element that has
            // cumulative weight <= sample_weight, then the next one will
            // be "it". (Note that this greatest element will never be the
            // last element of the vector, since sample_weight is chosen
            // in [0, total_weight) and the cumulative weight of the last
            // one is exactly the total weight.)
            while modifier > 1 {
                let i = idx + modifier / 2;
                if self.items[i].weight <= sample_weight {
                    // we're small, so look to the right, but allow this
                    // exact element still.
                    idx = i;
                    // we need the `/ 2` to round up otherwise we'll drop
                    // the trailing elements when `modifier` is odd.
                    modifier += 1;
                } else {
                    // otherwise we're too big, so go left. (i.e. do
                    // nothing)
                }
                modifier /= 2;
            }
            return self.items[idx + 1].item.clone();
        }
    }

    mod ziggurat_tables;

    /// Sample a random number using the Ziggurat method (specifically the
    /// ZIGNOR variant from Doornik 2005). Most of the arguments are
    /// directly from the paper:
    ///
    /// * `rng`: source of randomness
    /// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
    /// * `X`: the $x_i$ abscissae.
    /// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
    /// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
    /// * `pdf`: the probability density function
    /// * `zero_case`: manual sampling from the tail when we chose the
    ///    bottom box (i.e. i == 0)

    // the perf improvement (25-50%) is definitely worth the extra code
    // size from force-inlining.
    #[inline(always)]
    fn ziggurat<R: Rng, P, Z>(
                rng: &mut R,
                symmetric: bool,
                x_tab: ziggurat_tables::ZigTable,
                f_tab: ziggurat_tables::ZigTable,
                mut pdf: P,
                mut zero_case: Z)
                -> f64 where P: FnMut(f64) -> f64, Z: FnMut(&mut R, f64) -> f64 {
        const SCALE: f64 = (1u64 << 53) as f64;
        loop {
            // reimplement the f64 generation as an optimisation suggested
            // by the Doornik paper: we have a lot of precision-space
            // (i.e. there are 11 bits of the 64 of a u64 to use after
            // creating a f64), so we might as well reuse some to save
            // generating a whole extra random number. (Seems to be 15%
            // faster.)
            //
            // This unfortunately misses out on the benefits of direct
            // floating point generation if an RNG like dSMFT is
            // used. (That is, such RNGs create floats directly, highly
            // efficiently and overload next_f32/f64, so by not calling it
            // this may be slower than it would be otherwise.)
            // FIXME: investigate/optimise for the above.
            let bits: u64 = rng.gen();
            let i = (bits & 0xff) as usize;
            let f = (bits >> 11) as f64 / SCALE;

            // u is either U(-1, 1) or U(0, 1) depending on if this is a
            // symmetric distribution or not.
            let u = if symmetric {2.0 * f - 1.0} else {f};
            let x = u * x_tab[i];

            let test_x = if symmetric { x.abs() } else {x};

            // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
            if test_x < x_tab[i + 1] {
                return x;
            }
            if i == 0 {
                return zero_case(rng, u);
            }
            // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
            if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
                return x;
            }
        }
    }

    #[cfg(test)]
    mod tests {

        use {Rng, Rand};
        use super::{RandSample, WeightedChoice, Weighted, Sample, IndependentSample};

        #[derive(PartialEq, Debug)]
        struct ConstRand(usize);
        impl Rand for ConstRand {
            fn rand<R: Rng>(_: &mut R) -> ConstRand {
                ConstRand(0)
            }
        }

        // 0, 1, 2, 3, ...
        struct CountingRng { i: u32 }
        impl Rng for CountingRng {
            fn next_u32(&mut self) -> u32 {
                self.i += 1;
                self.i - 1
            }
            fn next_u64(&mut self) -> u64 {
                self.next_u32() as u64
            }
        }

        #[test]
        fn test_rand_sample() {
            let mut rand_sample = RandSample::<ConstRand>::new();

            assert_eq!(rand_sample.sample(&mut ::test::rng()), ConstRand(0));
            assert_eq!(rand_sample.ind_sample(&mut ::test::rng()), ConstRand(0));
        }
        #[test]
        fn test_weighted_choice() {
            // this makes assumptions about the internal implementation of
            // WeightedChoice, specifically: it doesn't reorder the items,
            // it doesn't do weird things to the RNG (so 0 maps to 0, 1 to
            // 1, internally; modulo a modulo operation).

            macro_rules! t {
                ($items:expr, $expected:expr) => {{
                    let mut items = $items;
                    let wc = WeightedChoice::new(&mut items);
                    let expected = $expected;

                    let mut rng = CountingRng { i: 0 };

                    for &val in expected.iter() {
                        assert_eq!(wc.ind_sample(&mut rng), val)
                    }
                }}
            }

            t!(vec!(Weighted { weight: 1, item: 10}), [10]);

            // skip some
            t!(vec!(Weighted { weight: 0, item: 20},
                    Weighted { weight: 2, item: 21},
                    Weighted { weight: 0, item: 22},
                    Weighted { weight: 1, item: 23}),
               [21,21, 23]);

            // different weights
            t!(vec!(Weighted { weight: 4, item: 30},
                    Weighted { weight: 3, item: 31}),
               [30,30,30,30, 31,31,31]);

            // check that we're binary searching
            // correctly with some vectors of odd
            // length.
            t!(vec!(Weighted { weight: 1, item: 40},
                    Weighted { weight: 1, item: 41},
                    Weighted { weight: 1, item: 42},
                    Weighted { weight: 1, item: 43},
                    Weighted { weight: 1, item: 44}),
               [40, 41, 42, 43, 44]);
            t!(vec!(Weighted { weight: 1, item: 50},
                    Weighted { weight: 1, item: 51},
                    Weighted { weight: 1, item: 52},
                    Weighted { weight: 1, item: 53},
                    Weighted { weight: 1, item: 54},
                    Weighted { weight: 1, item: 55},
                    Weighted { weight: 1, item: 56}),
               [50, 51, 52, 53, 54, 55, 56]);
        }

        #[test]
        fn test_weighted_clone_initialization() {
            let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
            let clone = initial.clone();
            assert_eq!(initial.weight, clone.weight);
            assert_eq!(initial.item, clone.item);
        }

        #[test] #[should_panic]
        #[cfg_attr(target_env = "msvc", ignore)]
        fn test_weighted_clone_change_weight() {
            let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
            let mut clone = initial.clone();
            clone.weight = 5;
            assert_eq!(initial.weight, clone.weight);
        }

        #[test] #[should_panic]
        #[cfg_attr(target_env = "msvc", ignore)]
        fn test_weighted_clone_change_item() {
            let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
            let mut clone = initial.clone();
            clone.item = 5;
            assert_eq!(initial.item, clone.item);

        }

        #[test] #[should_panic]
        #[cfg_attr(target_env = "msvc", ignore)]
        fn test_weighted_choice_no_items() {
            WeightedChoice::<isize>::new(&mut []);
        }
        #[test] #[should_panic]
        #[cfg_attr(target_env = "msvc", ignore)]
        fn test_weighted_choice_zero_weight() {
            WeightedChoice::new(&mut [Weighted { weight: 0, item: 0},
                                      Weighted { weight: 0, item: 1}]);
        }
        #[test] #[should_panic]
        #[cfg_attr(target_env = "msvc", ignore)]
        fn test_weighted_choice_weight_overflows() {
            let x = ::std::u32::MAX / 2; // x + x + 2 is the overflow
            WeightedChoice::new(&mut [Weighted { weight: x, item: 0 },
                                      Weighted { weight: 1, item: 1 },
                                      Weighted { weight: x, item: 2 },
                                      Weighted { weight: 1, item: 3 }]);
        }
    }

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