# index.rs - source
Source of the Rust file `/home/key/.cargo/registry/src/github.com-1ecc6299db9ec823/rand-0.8.5/src/seq/index.rs`.
Keywords: rust, rustlang, rust-lang

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    // Copyright 2018 Developers of the Rand project.
    //
    // 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.

    //! Low-level API for sampling indices

    #[cfg(feature = "alloc")] use core::slice;

    #[cfg(feature = "alloc")] use alloc::vec::{self, Vec};
    // BTreeMap is not as fast in tests, but better than nothing.
    #[cfg(all(feature = "alloc", not(feature = "std")))]
    use alloc::collections::BTreeSet;
    #[cfg(feature = "std")] use std::collections::HashSet;

    #[cfg(feature = "std")]
    use crate::distributions::WeightedError;

    #[cfg(feature = "alloc")]
    use crate::{Rng, distributions::{uniform::SampleUniform, Distribution, Uniform}};

    #[cfg(feature = "serde1")]
    use serde::{Serialize, Deserialize};

    /// A vector of indices.
    ///
    /// Multiple internal representations are possible.
    #[derive(Clone, Debug)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    pub enum IndexVec {
        #[doc(hidden)]
        U32(Vec<u32>),
        #[doc(hidden)]
        USize(Vec<usize>),
    }

    impl IndexVec {
        /// Returns the number of indices
        #[inline]
        pub fn len(&self) -> usize {
            match *self {
                IndexVec::U32(ref v) => v.len(),
                IndexVec::USize(ref v) => v.len(),
            }
        }

        /// Returns `true` if the length is 0.
        #[inline]
        pub fn is_empty(&self) -> bool {
            match *self {
                IndexVec::U32(ref v) => v.is_empty(),
                IndexVec::USize(ref v) => v.is_empty(),
            }
        }

        /// Return the value at the given `index`.
        ///
        /// (Note: we cannot implement [`std::ops::Index`] because of lifetime
        /// restrictions.)
        #[inline]
        pub fn index(&self, index: usize) -> usize {
            match *self {
                IndexVec::U32(ref v) => v[index] as usize,
                IndexVec::USize(ref v) => v[index],
            }
        }

        /// Return result as a `Vec<usize>`. Conversion may or may not be trivial.
        #[inline]
        pub fn into_vec(self) -> Vec<usize> {
            match self {
                IndexVec::U32(v) => v.into_iter().map(|i| i as usize).collect(),
                IndexVec::USize(v) => v,
            }
        }

        /// Iterate over the indices as a sequence of `usize` values
        #[inline]
        pub fn iter(&self) -> IndexVecIter<'_> {
            match *self {
                IndexVec::U32(ref v) => IndexVecIter::U32(v.iter()),
                IndexVec::USize(ref v) => IndexVecIter::USize(v.iter()),
            }
        }
    }

    impl IntoIterator for IndexVec {
        type Item = usize;
        type IntoIter = IndexVecIntoIter;

        /// Convert into an iterator over the indices as a sequence of `usize` values
        #[inline]
        fn into_iter(self) -> IndexVecIntoIter {
            match self {
                IndexVec::U32(v) => IndexVecIntoIter::U32(v.into_iter()),
                IndexVec::USize(v) => IndexVecIntoIter::USize(v.into_iter()),
            }
        }
    }

    impl PartialEq for IndexVec {
        fn eq(&self, other: &IndexVec) -> bool {
            use self::IndexVec::*;
            match (self, other) {
                (&U32(ref v1), &U32(ref v2)) => v1 == v2,
                (&USize(ref v1), &USize(ref v2)) => v1 == v2,
                (&U32(ref v1), &USize(ref v2)) => {
                    (v1.len() == v2.len()) && (v1.iter().zip(v2.iter()).all(|(x, y)| *x as usize == *y))
                }
                (&USize(ref v1), &U32(ref v2)) => {
                    (v1.len() == v2.len()) && (v1.iter().zip(v2.iter()).all(|(x, y)| *x == *y as usize))
                }
            }
        }
    }

    impl From<Vec<u32>> for IndexVec {
        #[inline]
        fn from(v: Vec<u32>) -> Self {
            IndexVec::U32(v)
        }
    }

    impl From<Vec<usize>> for IndexVec {
        #[inline]
        fn from(v: Vec<usize>) -> Self {
            IndexVec::USize(v)
        }
    }

    /// Return type of `IndexVec::iter`.
    #[derive(Debug)]
    pub enum IndexVecIter<'a> {
        #[doc(hidden)]
        U32(slice::Iter<'a, u32>),
        #[doc(hidden)]
        USize(slice::Iter<'a, usize>),
    }

    impl<'a> Iterator for IndexVecIter<'a> {
        type Item = usize;

        #[inline]
        fn next(&mut self) -> Option<usize> {
            use self::IndexVecIter::*;
            match *self {
                U32(ref mut iter) => iter.next().map(|i| *i as usize),
                USize(ref mut iter) => iter.next().cloned(),
            }
        }

        #[inline]
        fn size_hint(&self) -> (usize, Option<usize>) {
            match *self {
                IndexVecIter::U32(ref v) => v.size_hint(),
                IndexVecIter::USize(ref v) => v.size_hint(),
            }
        }
    }

    impl<'a> ExactSizeIterator for IndexVecIter<'a> {}

    /// Return type of `IndexVec::into_iter`.
    #[derive(Clone, Debug)]
    pub enum IndexVecIntoIter {
        #[doc(hidden)]
        U32(vec::IntoIter<u32>),
        #[doc(hidden)]
        USize(vec::IntoIter<usize>),
    }

    impl Iterator for IndexVecIntoIter {
        type Item = usize;

        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            use self::IndexVecIntoIter::*;
            match *self {
                U32(ref mut v) => v.next().map(|i| i as usize),
                USize(ref mut v) => v.next(),
            }
        }

        #[inline]
        fn size_hint(&self) -> (usize, Option<usize>) {
            use self::IndexVecIntoIter::*;
            match *self {
                U32(ref v) => v.size_hint(),
                USize(ref v) => v.size_hint(),
            }
        }
    }

    impl ExactSizeIterator for IndexVecIntoIter {}

    /// Randomly sample exactly `amount` distinct indices from `0..length`, and
    /// return them in random order (fully shuffled).
    ///
    /// This method is used internally by the slice sampling methods, but it can
    /// sometimes be useful to have the indices themselves so this is provided as
    /// an alternative.
    ///
    /// The implementation used is not specified; we automatically select the
    /// fastest available algorithm for the `length` and `amount` parameters
    /// (based on detailed profiling on an Intel Haswell CPU). Roughly speaking,
    /// complexity is `O(amount)`, except that when `amount` is small, performance
    /// is closer to `O(amount^2)`, and when `length` is close to `amount` then
    /// `O(length)`.
    ///
    /// Note that performance is significantly better over `u32` indices than over
    /// `u64` indices. Because of this we hide the underlying type behind an
    /// abstraction, `IndexVec`.
    ///
    /// If an allocation-free `no_std` function is required, it is suggested
    /// to adapt the internal `sample_floyd` implementation.
    ///
    /// Panics if `amount > length`.
    pub fn sample<R>(rng: &mut R, length: usize, amount: usize) -> IndexVec
    where R: Rng + ?Sized {
        if amount > length {
            panic!("`amount` of samples must be less than or equal to `length`");
        }
        if length > (::core::u32::MAX as usize) {
            // We never want to use inplace here, but could use floyd's alg
            // Lazy version: always use the cache alg.
            return sample_rejection(rng, length, amount);
        }
        let amount = amount as u32;
        let length = length as u32;

        // Choice of algorithm here depends on both length and amount. See:
        // https://github.com/rust-random/rand/pull/479
        // We do some calculations with f32. Accuracy is not very important.

        if amount < 163 {
            const C: [[f32; 2]; 2] = [[1.6, 8.0 / 45.0], [10.0, 70.0 / 9.0]];
            let j = if length < 500_000 { 0 } else { 1 };
            let amount_fp = amount as f32;
            let m4 = C[0][j] * amount_fp;
            // Short-cut: when amount < 12, floyd's is always faster
            if amount > 11 && (length as f32) < (C[1][j] + m4) * amount_fp {
                sample_inplace(rng, length, amount)
            } else {
                sample_floyd(rng, length, amount)
            }
        } else {
            const C: [f32; 2] = [270.0, 330.0 / 9.0];
            let j = if length < 500_000 { 0 } else { 1 };
            if (length as f32) < C[j] * (amount as f32) {
                sample_inplace(rng, length, amount)
            } else {
                sample_rejection(rng, length, amount)
            }
        }
    }

    /// Randomly sample exactly `amount` distinct indices from `0..length`, and
    /// return them in an arbitrary order (there is no guarantee of shuffling or
    /// ordering). The weights are to be provided by the input function `weights`,
    /// which will be called once for each index.
    ///
    /// This method is used internally by the slice sampling methods, but it can
    /// sometimes be useful to have the indices themselves so this is provided as
    /// an alternative.
    ///
    /// This implementation uses `O(length + amount)` space and `O(length)` time
    /// if the "nightly" feature is enabled, or `O(length)` space and
    /// `O(length + amount * log length)` time otherwise.
    ///
    /// Panics if `amount > length`.
    #[cfg(feature = "std")]
    #[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
    pub fn sample_weighted<R, F, X>(
        rng: &mut R, length: usize, weight: F, amount: usize,
    ) -> Result<IndexVec, WeightedError>
    where
        R: Rng + ?Sized,
        F: Fn(usize) -> X,
        X: Into<f64>,
    {
        if length > (core::u32::MAX as usize) {
            sample_efraimidis_spirakis(rng, length, weight, amount)
        } else {
            assert!(amount <= core::u32::MAX as usize);
            let amount = amount as u32;
            let length = length as u32;
            sample_efraimidis_spirakis(rng, length, weight, amount)
        }
    }

    /// Randomly sample exactly `amount` distinct indices from `0..length`, and
    /// return them in an arbitrary order (there is no guarantee of shuffling or
    /// ordering). The weights are to be provided by the input function `weights`,
    /// which will be called once for each index.
    ///
    /// This implementation uses the algorithm described by Efraimidis and Spirakis
    /// in this paper: https://doi.org/10.1016/j.ipl.2005.11.003
    /// It uses `O(length + amount)` space and `O(length)` time if the
    /// "nightly" feature is enabled, or `O(length)` space and `O(length
    /// + amount * log length)` time otherwise.
    ///
    /// Panics if `amount > length`.
    #[cfg(feature = "std")]
    fn sample_efraimidis_spirakis<R, F, X, N>(
        rng: &mut R, length: N, weight: F, amount: N,
    ) -> Result<IndexVec, WeightedError>
    where
        R: Rng + ?Sized,
        F: Fn(usize) -> X,
        X: Into<f64>,
        N: UInt,
        IndexVec: From<Vec<N>>,
    {
        if amount == N::zero() {
            return Ok(IndexVec::U32(Vec::new()));
        }

        if amount > length {
            panic!("`amount` of samples must be less than or equal to `length`");
        }

        struct Element<N> {
            index: N,
            key: f64,
        }
        impl<N> PartialOrd for Element<N> {
            fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
                self.key.partial_cmp(&other.key)
            }
        }
        impl<N> Ord for Element<N> {
            fn cmp(&self, other: &Self) -> core::cmp::Ordering {
                 // partial_cmp will always produce a value,
                 // because we check that the weights are not nan
                self.partial_cmp(other).unwrap()
            }
        }
        impl<N> PartialEq for Element<N> {
            fn eq(&self, other: &Self) -> bool {
                self.key == other.key
            }
        }
        impl<N> Eq for Element<N> {}

        #[cfg(feature = "nightly")]
        {
            let mut candidates = Vec::with_capacity(length.as_usize());
            let mut index = N::zero();
            while index < length {
                let weight = weight(index.as_usize()).into();
                if !(weight >= 0.) {
                    return Err(WeightedError::InvalidWeight);
                }

                let key = rng.gen::<f64>().powf(1.0 / weight);
                candidates.push(Element { index, key });

                index += N::one();
            }

            // Partially sort the array to find the `amount` elements with the greatest
            // keys. Do this by using `select_nth_unstable` to put the elements with
            // the *smallest* keys at the beginning of the list in `O(n)` time, which
            // provides equivalent information about the elements with the *greatest* keys.
            let (_, mid, greater)
                = candidates.select_nth_unstable(length.as_usize() - amount.as_usize());

            let mut result: Vec<N> = Vec::with_capacity(amount.as_usize());
            result.push(mid.index);
            for element in greater {
                result.push(element.index);
            }
            Ok(IndexVec::from(result))
        }

        #[cfg(not(feature = "nightly"))]
        {
            use alloc::collections::BinaryHeap;

            // Partially sort the array such that the `amount` elements with the largest
            // keys are first using a binary max heap.
            let mut candidates = BinaryHeap::with_capacity(length.as_usize());
            let mut index = N::zero();
            while index < length {
                let weight = weight(index.as_usize()).into();
                if !(weight >= 0.) {
                    return Err(WeightedError::InvalidWeight);
                }

                let key = rng.gen::<f64>().powf(1.0 / weight);
                candidates.push(Element { index, key });

                index += N::one();
            }

            let mut result: Vec<N> = Vec::with_capacity(amount.as_usize());
            while result.len() < amount.as_usize() {
                result.push(candidates.pop().unwrap().index);
            }
            Ok(IndexVec::from(result))
        }
    }

    /// Randomly sample exactly `amount` indices from `0..length`, using Floyd's
    /// combination algorithm.
    ///
    /// The output values are fully shuffled. (Overhead is under 50%.)
    ///
    /// This implementation uses `O(amount)` memory and `O(amount^2)` time.
    fn sample_floyd<R>(rng: &mut R, length: u32, amount: u32) -> IndexVec
    where R: Rng + ?Sized {
        // For small amount we use Floyd's fully-shuffled variant. For larger
        // amounts this is slow due to Vec::insert performance, so we shuffle
        // afterwards. Benchmarks show little overhead from extra logic.
        let floyd_shuffle = amount < 50;

        debug_assert!(amount <= length);
        let mut indices = Vec::with_capacity(amount as usize);
        for j in length - amount..length {
            let t = rng.gen_range(0..=j);
            if floyd_shuffle {
                if let Some(pos) = indices.iter().position(|&x| x == t) {
                    indices.insert(pos, j);
                    continue;
                }
            } else if indices.contains(&t) {
                indices.push(j);
                continue;
            }
            indices.push(t);
        }
        if !floyd_shuffle {
            // Reimplement SliceRandom::shuffle with smaller indices
            for i in (1..amount).rev() {
                // invariant: elements with index > i have been locked in place.
                indices.swap(i as usize, rng.gen_range(0..=i) as usize);
            }
        }
        IndexVec::from(indices)
    }

    /// Randomly sample exactly `amount` indices from `0..length`, using an inplace
    /// partial Fisher-Yates method.
    /// Sample an amount of indices using an inplace partial fisher yates method.
    ///
    /// This allocates the entire `length` of indices and randomizes only the first `amount`.
    /// It then truncates to `amount` and returns.
    ///
    /// This method is not appropriate for large `length` and potentially uses a lot
    /// of memory; because of this we only implement for `u32` index (which improves
    /// performance in all cases).
    ///
    /// Set-up is `O(length)` time and memory and shuffling is `O(amount)` time.
    fn sample_inplace<R>(rng: &mut R, length: u32, amount: u32) -> IndexVec
    where R: Rng + ?Sized {
        debug_assert!(amount <= length);
        let mut indices: Vec<u32> = Vec::with_capacity(length as usize);
        indices.extend(0..length);
        for i in 0..amount {
            let j: u32 = rng.gen_range(i..length);
            indices.swap(i as usize, j as usize);
        }
        indices.truncate(amount as usize);
        debug_assert_eq!(indices.len(), amount as usize);
        IndexVec::from(indices)
    }

    trait UInt: Copy + PartialOrd + Ord + PartialEq + Eq + SampleUniform
        + core::hash::Hash + core::ops::AddAssign {
        fn zero() -> Self;
        fn one() -> Self;
        fn as_usize(self) -> usize;
    }
    impl UInt for u32 {
        #[inline]
        fn zero() -> Self {
            0
        }

        #[inline]
        fn one() -> Self {
            1
        }

        #[inline]
        fn as_usize(self) -> usize {
            self as usize
        }
    }
    impl UInt for usize {
        #[inline]
        fn zero() -> Self {
            0
        }

        #[inline]
        fn one() -> Self {
            1
        }

        #[inline]
        fn as_usize(self) -> usize {
            self
        }
    }

    /// Randomly sample exactly `amount` indices from `0..length`, using rejection
    /// sampling.
    ///
    /// Since `amount <<< length` there is a low chance of a random sample in
    /// `0..length` being a duplicate. We test for duplicates and resample where
    /// necessary. The algorithm is `O(amount)` time and memory.
    ///
    /// This function  is generic over X primarily so that results are value-stable
    /// over 32-bit and 64-bit platforms.
    fn sample_rejection<X: UInt, R>(rng: &mut R, length: X, amount: X) -> IndexVec
    where
        R: Rng + ?Sized,
        IndexVec: From<Vec<X>>,
    {
        debug_assert!(amount < length);
        #[cfg(feature = "std")]
        let mut cache = HashSet::with_capacity(amount.as_usize());
        #[cfg(not(feature = "std"))]
        let mut cache = BTreeSet::new();
        let distr = Uniform::new(X::zero(), length);
        let mut indices = Vec::with_capacity(amount.as_usize());
        for _ in 0..amount.as_usize() {
            let mut pos = distr.sample(rng);
            while !cache.insert(pos) {
                pos = distr.sample(rng);
            }
            indices.push(pos);
        }

        debug_assert_eq!(indices.len(), amount.as_usize());
        IndexVec::from(indices)
    }

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

        #[test]
        #[cfg(feature = "serde1")]
        fn test_serialization_index_vec() {
            let some_index_vec = IndexVec::from(vec![254_usize, 234, 2, 1]);
            let de_some_index_vec: IndexVec = bincode::deserialize(&bincode::serialize(&some_index_vec).unwrap()).unwrap();
            match (some_index_vec, de_some_index_vec) {
                (IndexVec::U32(a), IndexVec::U32(b)) => {
                    assert_eq!(a, b);
                },
                (IndexVec::USize(a), IndexVec::USize(b)) => {
                    assert_eq!(a, b);
                },
                _ => {panic!("failed to seralize/deserialize `IndexVec`")}
            }
        }

        #[cfg(feature = "alloc")] use alloc::vec;

        #[test]
        fn test_sample_boundaries() {
            let mut r = crate::test::rng(404);

            assert_eq!(sample_inplace(&mut r, 0, 0).len(), 0);
            assert_eq!(sample_inplace(&mut r, 1, 0).len(), 0);
            assert_eq!(sample_inplace(&mut r, 1, 1).into_vec(), vec![0]);

            assert_eq!(sample_rejection(&mut r, 1u32, 0).len(), 0);

            assert_eq!(sample_floyd(&mut r, 0, 0).len(), 0);
            assert_eq!(sample_floyd(&mut r, 1, 0).len(), 0);
            assert_eq!(sample_floyd(&mut r, 1, 1).into_vec(), vec![0]);

            // These algorithms should be fast with big numbers. Test average.
            let sum: usize = sample_rejection(&mut r, 1 << 25, 10u32).into_iter().sum();
            assert!(1 << 25 < sum && sum < (1 << 25) * 25);

            let sum: usize = sample_floyd(&mut r, 1 << 25, 10).into_iter().sum();
            assert!(1 << 25 < sum && sum < (1 << 25) * 25);
        }

        #[test]
        #[cfg_attr(miri, ignore)] // Miri is too slow
        fn test_sample_alg() {
            let seed_rng = crate::test::rng;

            // We can't test which algorithm is used directly, but Floyd's alg
            // should produce different results from the others. (Also, `inplace`
            // and `cached` currently use different sizes thus produce different results.)

            // A small length and relatively large amount should use inplace
            let (length, amount): (usize, usize) = (100, 50);
            let v1 = sample(&mut seed_rng(420), length, amount);
            let v2 = sample_inplace(&mut seed_rng(420), length as u32, amount as u32);
            assert!(v1.iter().all(|e| e < length));
            assert_eq!(v1, v2);

            // Test Floyd's alg does produce different results
            let v3 = sample_floyd(&mut seed_rng(420), length as u32, amount as u32);
            assert!(v1 != v3);

            // A large length and small amount should use Floyd
            let (length, amount): (usize, usize) = (1 << 20, 50);
            let v1 = sample(&mut seed_rng(421), length, amount);
            let v2 = sample_floyd(&mut seed_rng(421), length as u32, amount as u32);
            assert!(v1.iter().all(|e| e < length));
            assert_eq!(v1, v2);

            // A large length and larger amount should use cache
            let (length, amount): (usize, usize) = (1 << 20, 600);
            let v1 = sample(&mut seed_rng(422), length, amount);
            let v2 = sample_rejection(&mut seed_rng(422), length as u32, amount as u32);
            assert!(v1.iter().all(|e| e < length));
            assert_eq!(v1, v2);
        }

        #[cfg(feature = "std")]
        #[test]
        fn test_sample_weighted() {
            let seed_rng = crate::test::rng;
            for &(amount, len) in &[(0, 10), (5, 10), (10, 10)] {
                let v = sample_weighted(&mut seed_rng(423), len, |i| i as f64, amount).unwrap();
                match v {
                    IndexVec::U32(mut indices) => {
                        assert_eq!(indices.len(), amount);
                        indices.sort_unstable();
                        indices.dedup();
                        assert_eq!(indices.len(), amount);
                        for &i in &indices {
                            assert!((i as usize) < len);
                        }
                    },
                    IndexVec::USize(_) => panic!("expected `IndexVec::U32`"),
                }
            }
        }

        #[test]
        fn value_stability_sample() {
            let do_test = |length, amount, values: &[u32]| {
                let mut buf = [0u32; 8];
                let mut rng = crate::test::rng(410);

                let res = sample(&mut rng, length, amount);
                let len = res.len().min(buf.len());
                for (x, y) in res.into_iter().zip(buf.iter_mut()) {
                    *y = x as u32;
                }
                assert_eq!(
                    &buf[0..len],
                    values,
                    "failed sampling {}, {}",
                    length,
                    amount
                );
            };

            do_test(10, 6, &[8, 0, 3, 5, 9, 6]); // floyd
            do_test(25, 10, &[18, 15, 14, 9, 0, 13, 5, 24]); // floyd
            do_test(300, 8, &[30, 283, 150, 1, 73, 13, 285, 35]); // floyd
            do_test(300, 80, &[31, 289, 248, 154, 5, 78, 19, 286]); // inplace
            do_test(300, 180, &[31, 289, 248, 154, 5, 78, 19, 286]); // inplace

            do_test(1_000_000, 8, &[
                103717, 963485, 826422, 509101, 736394, 807035, 5327, 632573,
            ]); // floyd
            do_test(1_000_000, 180, &[
                103718, 963490, 826426, 509103, 736396, 807036, 5327, 632573,
            ]); // rejection
        }
    }