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    //! This module contains an implementation of alias method for sampling random
    //! indices with probabilities proportional to a collection of weights.

    use super::WeightedError;
    #[cfg(not(feature = "std"))]
    use crate::alloc::vec::Vec;
    #[cfg(not(feature = "std"))]
    use crate::alloc::vec;
    use core::fmt;
    use core::iter::Sum;
    use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};
    use crate::distributions::uniform::SampleUniform;
    use crate::distributions::Distribution;
    use crate::distributions::Uniform;
    use crate::Rng;

    /// A distribution using weighted sampling to pick a discretely selected item.
    ///
    /// Sampling a [`WeightedIndex<W>`] distribution returns the index of a randomly
    /// selected element from the vector used to create the [`WeightedIndex<W>`].
    /// The chance of a given element being picked is proportional to the value of
    /// the element. The weights can have any type `W` for which a implementation of
    /// [`Weight`] exists.
    ///
    /// # Performance
    ///
    /// Given that `n` is the number of items in the vector used to create an
    /// [`WeightedIndex<W>`], [`WeightedIndex<W>`] will require `O(n)` amount of
    /// memory. More specifically it takes up some constant amount of memory plus
    /// the vector used to create it and a [`Vec<u32>`] with capacity `n`.
    ///
    /// Time complexity for the creation of a [`WeightedIndex<W>`] is `O(n)`.
    /// Sampling is `O(1)`, it makes a call to [`Uniform<u32>::sample`] and a call
    /// to [`Uniform<W>::sample`].
    ///
    /// # Example
    ///
    /// ```
    /// use rand::distributions::weighted::alias_method::WeightedIndex;
    /// use rand::prelude::*;
    ///
    /// let choices = vec!['a', 'b', 'c'];
    /// let weights = vec![2, 1, 1];
    /// let dist = WeightedIndex::new(weights).unwrap();
    /// let mut rng = thread_rng();
    /// for _ in 0..100 {
    ///     // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'
    ///     println!("{}", choices[dist.sample(&mut rng)]);
    /// }
    ///
    /// let items = [('a', 0), ('b', 3), ('c', 7)];
    /// let dist2 = WeightedIndex::new(items.iter().map(|item| item.1).collect()).unwrap();
    /// for _ in 0..100 {
    ///     // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'
    ///     println!("{}", items[dist2.sample(&mut rng)].0);
    /// }
    /// ```
    ///
    /// [`WeightedIndex<W>`]: crate::distributions::weighted::alias_method::WeightedIndex
    /// [`Weight`]: crate::distributions::weighted::alias_method::Weight
    /// [`Vec<u32>`]: Vec
    /// [`Uniform<u32>::sample`]: Distribution::sample
    /// [`Uniform<W>::sample`]: Distribution::sample
    pub struct WeightedIndex<W: Weight> {
        aliases: Vec<u32>,
        no_alias_odds: Vec<W>,
        uniform_index: Uniform<u32>,
        uniform_within_weight_sum: Uniform<W>,
    }

    impl<W: Weight> WeightedIndex<W> {
        /// Creates a new [`WeightedIndex`].
        ///
        /// Returns an error if:
        /// - The vector is empty.
        /// - The vector is longer than `u32::MAX`.
        /// - For any weight `w`: `w < 0` or `w > max` where `max = W::MAX /
        ///   weights.len()`.
        /// - The sum of weights is zero.
        pub fn new(weights: Vec<W>) -> Result<Self, WeightedError> {
            let n = weights.len();
            if n == 0 {
                return Err(WeightedError::NoItem);
            } else if n > ::core::u32::MAX as usize {
                return Err(WeightedError::TooMany);
            }
            let n = n as u32;

            let max_weight_size = W::try_from_u32_lossy(n)
                .map(|n| W::MAX / n)
                .unwrap_or(W::ZERO);
            if !weights
                .iter()
                .all(|&w| W::ZERO <= w && w <= max_weight_size)
            {
                return Err(WeightedError::InvalidWeight);
            }

            // The sum of weights will represent 100% of no alias odds.
            let weight_sum = Weight::sum(weights.as_slice());
            // Prevent floating point overflow due to rounding errors.
            let weight_sum = if weight_sum > W::MAX {
                W::MAX
            } else {
                weight_sum
            };
            if weight_sum == W::ZERO {
                return Err(WeightedError::AllWeightsZero);
            }

            // `weight_sum` would have been zero if `try_from_lossy` causes an error here.
            let n_converted = W::try_from_u32_lossy(n).unwrap();

            let mut no_alias_odds = weights;
            for odds in no_alias_odds.iter_mut() {
                *odds *= n_converted;
                // Prevent floating point overflow due to rounding errors.
                *odds = if *odds > W::MAX { W::MAX } else { *odds };
            }

            /// This struct is designed to contain three data structures at once,
            /// sharing the same memory. More precisely it contains two linked lists
            /// and an alias map, which will be the output of this method. To keep
            /// the three data structures from getting in each other's way, it must
            /// be ensured that a single index is only ever in one of them at the
            /// same time.
            struct Aliases {
                aliases: Vec<u32>,
                smalls_head: u32,
                bigs_head: u32,
            }

            impl Aliases {
                fn new(size: u32) -> Self {
                    Aliases {
                        aliases: vec![0; size as usize],
                        smalls_head: ::core::u32::MAX,
                        bigs_head: ::core::u32::MAX,
                    }
                }

                fn push_small(&mut self, idx: u32) {
                    self.aliases[idx as usize] = self.smalls_head;
                    self.smalls_head = idx;
                }

                fn push_big(&mut self, idx: u32) {
                    self.aliases[idx as usize] = self.bigs_head;
                    self.bigs_head = idx;
                }

                fn pop_small(&mut self) -> u32 {
                    let popped = self.smalls_head;
                    self.smalls_head = self.aliases[popped as usize];
                    popped
                }

                fn pop_big(&mut self) -> u32 {
                    let popped = self.bigs_head;
                    self.bigs_head = self.aliases[popped as usize];
                    popped
                }

                fn smalls_is_empty(&self) -> bool {
                    self.smalls_head == ::core::u32::MAX
                }

                fn bigs_is_empty(&self) -> bool {
                    self.bigs_head == ::core::u32::MAX
                }

                fn set_alias(&mut self, idx: u32, alias: u32) {
                    self.aliases[idx as usize] = alias;
                }
            }

            let mut aliases = Aliases::new(n);

            // Split indices into those with small weights and those with big weights.
            for (index, &odds) in no_alias_odds.iter().enumerate() {
                if odds < weight_sum {
                    aliases.push_small(index as u32);
                } else {
                    aliases.push_big(index as u32);
                }
            }

            // Build the alias map by finding an alias with big weight for each index with
            // small weight.
            while !aliases.smalls_is_empty() && !aliases.bigs_is_empty() {
                let s = aliases.pop_small();
                let b = aliases.pop_big();

                aliases.set_alias(s, b);
                no_alias_odds[b as usize] = no_alias_odds[b as usize]
                        - weight_sum
                        + no_alias_odds[s as usize];

                if no_alias_odds[b as usize] < weight_sum {
                    aliases.push_small(b);
                } else {
                    aliases.push_big(b);
                }
            }

            // The remaining indices should have no alias odds of about 100%. This is due to
            // numeric accuracy. Otherwise they would be exactly 100%.
            while !aliases.smalls_is_empty() {
                no_alias_odds[aliases.pop_small() as usize] = weight_sum;
            }
            while !aliases.bigs_is_empty() {
                no_alias_odds[aliases.pop_big() as usize] = weight_sum;
            }

            // Prepare distributions for sampling. Creating them beforehand improves
            // sampling performance.
            let uniform_index = Uniform::new(0, n);
            let uniform_within_weight_sum = Uniform::new(W::ZERO, weight_sum);

            Ok(Self {
                aliases: aliases.aliases,
                no_alias_odds,
                uniform_index,
                uniform_within_weight_sum,
            })
        }
    }

    impl<W: Weight> Distribution<usize> for WeightedIndex<W> {
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
            let candidate = rng.sample(self.uniform_index);
            if rng.sample(&self.uniform_within_weight_sum) < self.no_alias_odds[candidate as usize] {
                candidate as usize
            } else {
                self.aliases[candidate as usize] as usize
            }
        }
    }

    impl<W: Weight> fmt::Debug for WeightedIndex<W>
    where
        W: fmt::Debug,
        Uniform<W>: fmt::Debug,
    {
        fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
            f.debug_struct("WeightedIndex")
                .field("aliases", &self.aliases)
                .field("no_alias_odds", &self.no_alias_odds)
                .field("uniform_index", &self.uniform_index)
                .field("uniform_within_weight_sum", &self.uniform_within_weight_sum)
                .finish()
        }
    }

    impl<W: Weight> Clone for WeightedIndex<W>
    where
        Uniform<W>: Clone,
    {
        fn clone(&self) -> Self {
            Self {
                aliases: self.aliases.clone(),
                no_alias_odds: self.no_alias_odds.clone(),
                uniform_index: self.uniform_index.clone(),
                uniform_within_weight_sum: self.uniform_within_weight_sum.clone(),
            }
        }
    }

    /// Trait that must be implemented for weights, that are used with
    /// [`WeightedIndex`]. Currently no guarantees on the correctness of
    /// [`WeightedIndex`] are given for custom implementations of this trait.
    pub trait Weight:
        Sized
        + Copy
        + SampleUniform
        + PartialOrd
        + Add<Output = Self>
        + AddAssign
        + Sub<Output = Self>
        + SubAssign
        + Mul<Output = Self>
        + MulAssign
        + Div<Output = Self>
        + DivAssign
        + Sum
    {
        /// Maximum number representable by `Self`.
        const MAX: Self;

        /// Element of `Self` equivalent to 0.
        const ZERO: Self;

        /// Produce an instance of `Self` from a `u32` value, or return `None` if
        /// out of range. Loss of precision (where `Self` is a floating point type)
        /// is acceptable.
        fn try_from_u32_lossy(n: u32) -> Option<Self>;

        /// Sums all values in slice `values`.
        fn sum(values: &[Self]) -> Self {
            values.iter().map(|x| *x).sum()
        }
    }

    macro_rules! impl_weight_for_float {
        ($T: ident) => {
            impl Weight for $T {
                const MAX: Self = ::core::$T::MAX;
                const ZERO: Self = 0.0;

                fn try_from_u32_lossy(n: u32) -> Option<Self> {
                    Some(n as $T)
                }

                fn sum(values: &[Self]) -> Self {
                    pairwise_sum(values)
                }
            }
        };
    }

    /// In comparison to naive accumulation, the pairwise sum algorithm reduces
    /// rounding errors when there are many floating point values.
    fn pairwise_sum<T: Weight>(values: &[T]) -> T {
        if values.len() <= 32 {
            values.iter().map(|x| *x).sum()
        } else {
            let mid = values.len() / 2;
            let (a, b) = values.split_at(mid);
            pairwise_sum(a) + pairwise_sum(b)
        }
    }

    macro_rules! impl_weight_for_int {
        ($T: ident) => {
            impl Weight for $T {
                const MAX: Self = ::core::$T::MAX;
                const ZERO: Self = 0;

                fn try_from_u32_lossy(n: u32) -> Option<Self> {
                    let n_converted = n as Self;
                    if n_converted >= Self::ZERO && n_converted as u32 == n {
                        Some(n_converted)
                    } else {
                        None
                    }
                }
            }
        };
    }

    impl_weight_for_float!(f64);
    impl_weight_for_float!(f32);
    impl_weight_for_int!(usize);
    #[cfg(not(target_os = "emscripten"))]
    impl_weight_for_int!(u128);
    impl_weight_for_int!(u64);
    impl_weight_for_int!(u32);
    impl_weight_for_int!(u16);
    impl_weight_for_int!(u8);
    impl_weight_for_int!(isize);
    #[cfg(not(target_os = "emscripten"))]
    impl_weight_for_int!(i128);
    impl_weight_for_int!(i64);
    impl_weight_for_int!(i32);
    impl_weight_for_int!(i16);
    impl_weight_for_int!(i8);

    #[cfg(test)]
    mod test {
        use super::*;

        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_weighted_index_f32() {
            test_weighted_index(f32::into);

            // Floating point special cases
            assert_eq!(
                WeightedIndex::new(vec![::core::f32::INFINITY]).unwrap_err(),
                WeightedError::InvalidWeight
            );
            assert_eq!(
                WeightedIndex::new(vec![-0_f32]).unwrap_err(),
                WeightedError::AllWeightsZero
            );
            assert_eq!(
                WeightedIndex::new(vec![-1_f32]).unwrap_err(),
                WeightedError::InvalidWeight
            );
            assert_eq!(
                WeightedIndex::new(vec![-::core::f32::INFINITY]).unwrap_err(),
                WeightedError::InvalidWeight
            );
            assert_eq!(
                WeightedIndex::new(vec![::core::f32::NAN]).unwrap_err(),
                WeightedError::InvalidWeight
            );
        }

        #[cfg(not(target_os = "emscripten"))]
        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_weighted_index_u128() {
            test_weighted_index(|x: u128| x as f64);
        }

        #[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_weighted_index_i128() {
            test_weighted_index(|x: i128| x as f64);

            // Signed integer special cases
            assert_eq!(
                WeightedIndex::new(vec![-1_i128]).unwrap_err(),
                WeightedError::InvalidWeight
            );
            assert_eq!(
                WeightedIndex::new(vec![::core::i128::MIN]).unwrap_err(),
                WeightedError::InvalidWeight
            );
        }

        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_weighted_index_u8() {
            test_weighted_index(u8::into);
        }

        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_weighted_index_i8() {
            test_weighted_index(i8::into);

            // Signed integer special cases
            assert_eq!(
                WeightedIndex::new(vec![-1_i8]).unwrap_err(),
                WeightedError::InvalidWeight
            );
            assert_eq!(
                WeightedIndex::new(vec![::core::i8::MIN]).unwrap_err(),
                WeightedError::InvalidWeight
            );
        }

        fn test_weighted_index<W: Weight, F: Fn(W) -> f64>(w_to_f64: F)
        where
            WeightedIndex<W>: fmt::Debug,
        {
            const NUM_WEIGHTS: u32 = 10;
            const ZERO_WEIGHT_INDEX: u32 = 3;
            const NUM_SAMPLES: u32 = 15000;
            let mut rng = crate::test::rng(0x9c9fa0b0580a7031);

            let weights = {
                let mut weights = Vec::with_capacity(NUM_WEIGHTS as usize);
                let random_weight_distribution = crate::distributions::Uniform::new_inclusive(
                    W::ZERO,
                    W::MAX / W::try_from_u32_lossy(NUM_WEIGHTS).unwrap(),
                );
                for _ in 0..NUM_WEIGHTS {
                    weights.push(rng.sample(&random_weight_distribution));
                }
                weights[ZERO_WEIGHT_INDEX as usize] = W::ZERO;
                weights
            };
            let weight_sum = weights.iter().map(|w| *w).sum::<W>();
            let expected_counts = weights
                .iter()
                .map(|&w| w_to_f64(w) / w_to_f64(weight_sum) * NUM_SAMPLES as f64)
                .collect::<Vec<f64>>();
            let weight_distribution = WeightedIndex::new(weights).unwrap();

            let mut counts = vec![0; NUM_WEIGHTS as usize];
            for _ in 0..NUM_SAMPLES {
                counts[rng.sample(&weight_distribution)] += 1;
            }

            assert_eq!(counts[ZERO_WEIGHT_INDEX as usize], 0);
            for (count, expected_count) in counts.into_iter().zip(expected_counts) {
                let difference = (count as f64 - expected_count).abs();
                let max_allowed_difference = NUM_SAMPLES as f64 / NUM_WEIGHTS as f64 * 0.1;
                assert!(difference <= max_allowed_difference);
            }

            assert_eq!(
                WeightedIndex::<W>::new(vec![]).unwrap_err(),
                WeightedError::NoItem
            );
            assert_eq!(
                WeightedIndex::new(vec![W::ZERO]).unwrap_err(),
                WeightedError::AllWeightsZero
            );
            assert_eq!(
                WeightedIndex::new(vec![W::MAX, W::MAX]).unwrap_err(),
                WeightedError::InvalidWeight
            );
        }
    }

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