Add initial implementation of 'sort_at_index' for slices -- analog to C++'s std::nth_element (a.k.a. quickselect)

Add some more notes to the documentation:

- Mention that the median can be found if we used `len() / 2`.
- Mention that this function is usually called "kth element" in other libraries.

Address some comments in PR:

- Change wording on some of the documentation
- Change recursive function into a loop

Update name to `partition_at_index` and add convenience return values.

Address reviewer comments:

- Don't swap on each iteration when searching for min/max element.
- Add some docs about when we panic.
- Test that the sum of the lengths of the output matches the length of the input.
- Style fix for for-loop.

Address more reviewer comments

Fix Rng stuff for test

Fix doc test build

Don't run the partition_at_index test on wasm targets

Miri does not support entropy for test partition_at_index

src/libcore/slice/mod.rs

@@ -1585,6 +1585,153 @@ impl<T> [T] {
         sort::quicksort(self, |a, b| f(a).lt(&f(b)));
     }
 
+    /// Reorder the slice such that the element at `index` is at its final sorted position.
+    ///
+    /// This reordering has the additional property that any value at position `i < index` will be
+    /// less than or equal to any value at a position `j > index`. Additionally, this reordering is
+    /// unstable (i.e. any number of equal elements may end up at position `index`), in-place
+    /// (i.e. does not allocate), and `O(n)` worst-case. This function is also/ known as "kth
+    /// element" in other libraries. It returns a triplet of the following values: all elements less
+    /// than the one at the given index, the value at the given index, and all elements greater than
+    /// the one at the given index.
+    ///
+    /// # Current implementation
+    ///
+    /// The current algorithm is based on the quickselect portion of the same quicksort algorithm
+    /// used for [`sort_unstable`].
+    ///
+    /// [`sort_unstable`]: #method.sort_unstable
+    ///
+    /// # Panics
+    ///
+    /// Panics when `index >= len()`, meaning it always panics on empty slices.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// #![feature(slice_partition_at_index)]
+    ///
+    /// let mut v = [-5i32, 4, 1, -3, 2];
+    ///
+    /// // Find the median
+    /// v.partition_at_index(2);
+    ///
+    /// // We are only guaranteed the slice will be one of the following, based on the way we sort
+    /// // about the specified index.
+    /// assert!(v == [-3, -5, 1, 2, 4] ||
+    ///         v == [-5, -3, 1, 2, 4] ||
+    ///         v == [-3, -5, 1, 4, 2] ||
+    ///         v == [-5, -3, 1, 4, 2]);
+    /// ```
+    #[unstable(feature = "slice_partition_at_index", issue = "55300")]
+    #[inline]
+    pub fn partition_at_index(&mut self, index: usize) -> (&mut [T], &mut T, &mut [T])
+        where T: Ord
+    {
+        let mut f = |a: &T, b: &T| a.lt(b);
+        sort::partition_at_index(self, index, &mut f)
+    }
+
+    /// Reorder the slice with a comparator function such that the element at `index` is at its
+    /// final sorted position.
+    ///
+    /// This reordering has the additional property that any value at position `i < index` will be
+    /// less than or equal to any value at a position `j > index` using the comparator function.
+    /// Additionally, this reordering is unstable (i.e. any number of equal elements may end up at
+    /// position `index`), in-place (i.e. does not allocate), and `O(n)` worst-case. This function
+    /// is also known as "kth element" in other libraries. It returns a triplet of the following
+    /// values: all elements less than the one at the given index, the value at the given index,
+    /// and all elements greater than the one at the given index, using the provided comparator
+    /// function.
+    ///
+    /// # Current implementation
+    ///
+    /// The current algorithm is based on the quickselect portion of the same quicksort algorithm
+    /// used for [`sort_unstable`].
+    ///
+    /// [`sort_unstable`]: #method.sort_unstable
+    ///
+    /// # Panics
+    ///
+    /// Panics when `index >= len()`, meaning it always panics on empty slices.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// #![feature(slice_partition_at_index)]
+    ///
+    /// let mut v = [-5i32, 4, 1, -3, 2];
+    ///
+    /// // Find the median as if the slice were sorted in descending order.
+    /// v.partition_at_index_by(2, |a, b| b.cmp(a));
+    ///
+    /// // We are only guaranteed the slice will be one of the following, based on the way we sort
+    /// // about the specified index.
+    /// assert!(v == [2, 4, 1, -5, -3] ||
+    ///         v == [2, 4, 1, -3, -5] ||
+    ///         v == [4, 2, 1, -5, -3] ||
+    ///         v == [4, 2, 1, -3, -5]);
+    /// ```
+    #[unstable(feature = "slice_partition_at_index", issue = "55300")]
+    #[inline]
+    pub fn partition_at_index_by<F>(&mut self, index: usize, mut compare: F)
+                                    -> (&mut [T], &mut T, &mut [T])
+        where F: FnMut(&T, &T) -> Ordering
+    {
+        let mut f = |a: &T, b: &T| compare(a, b) == Less;
+        sort::partition_at_index(self, index, &mut f)
+    }
+
+    /// Reorder the slice with a key extraction function such that the element at `index` is at its
+    /// final sorted position.
+    ///
+    /// This reordering has the additional property that any value at position `i < index` will be
+    /// less than or equal to any value at a position `j > index` using the key extraction function.
+    /// Additionally, this reordering is unstable (i.e. any number of equal elements may end up at
+    /// position `index`), in-place (i.e. does not allocate), and `O(n)` worst-case. This function
+    /// is also known as "kth element" in other libraries. It returns a triplet of the following
+    /// values: all elements less than the one at the given index, the value at the given index, and
+    /// all elements greater than the one at the given index, using the provided key extraction
+    /// function.
+    ///
+    /// # Current implementation
+    ///
+    /// The current algorithm is based on the quickselect portion of the same quicksort algorithm
+    /// used for [`sort_unstable`].
+    ///
+    /// [`sort_unstable`]: #method.sort_unstable
+    ///
+    /// # Panics
+    ///
+    /// Panics when `index >= len()`, meaning it always panics on empty slices.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// #![feature(slice_partition_at_index)]
+    ///
+    /// let mut v = [-5i32, 4, 1, -3, 2];
+    ///
+    /// // Return the median as if the array were sorted according to absolute value.
+    /// v.partition_at_index_by_key(2, |a| a.abs());
+    ///
+    /// // We are only guaranteed the slice will be one of the following, based on the way we sort
+    /// // about the specified index.
+    /// assert!(v == [1, 2, -3, 4, -5] ||
+    ///         v == [1, 2, -3, -5, 4] ||
+    ///         v == [2, 1, -3, 4, -5] ||
+    ///         v == [2, 1, -3, -5, 4]);
+    /// ```
+    #[unstable(feature = "slice_partition_at_index", issue = "55300")]
+    #[inline]
+    pub fn partition_at_index_by_key<K, F>(&mut self, index: usize, mut f: F)
+                                           -> (&mut [T], &mut T, &mut [T])
+        where F: FnMut(&T) -> K, K: Ord
+    {
+        let mut g = |a: &T, b: &T| f(a).lt(&f(b));
+        sort::partition_at_index(self, index, &mut g)
+    }
+
     /// Moves all consecutive repeated elements to the end of the slice according to the
     /// [`PartialEq`] trait implementation.
     ///

src/libcore/slice/sort.rs

@@ -691,3 +691,92 @@ pub fn quicksort<T, F>(v: &mut [T], mut is_less: F)
 
     recurse(v, &mut is_less, None, limit);
 }
+
+fn partition_at_index_loop<'a, T, F>( mut v: &'a mut [T], mut index: usize, is_less: &mut F
+                                    , mut pred: Option<&'a T>) where F: FnMut(&T, &T) -> bool
+{
+    loop {
+        // For slices of up to this length it's probably faster to simply sort them.
+        const MAX_INSERTION: usize = 10;
+        if v.len() <= MAX_INSERTION {
+            insertion_sort(v, is_less);
+            return;
+        }
+
+        // Choose a pivot
+        let (pivot, _) = choose_pivot(v, is_less);
+
+        // If the chosen pivot is equal to the predecessor, then it's the smallest element in the
+        // slice. Partition the slice into elements equal to and elements greater than the pivot.
+        // This case is usually hit when the slice contains many duplicate elements.
+        if let Some(p) = pred {
+            if !is_less(p, &v[pivot]) {
+                let mid = partition_equal(v, pivot, is_less);
+
+                // If we've passed our index, then we're good.
+                if mid > index {
+                    return;
+                }
+
+                // Otherwise, continue sorting elements greater than the pivot.
+                v = &mut v[mid..];
+                index = index - mid;
+                pred = None;
+                continue;
+            }
+        }
+
+        let (mid, _) = partition(v, pivot, is_less);
+
+        // Split the slice into `left`, `pivot`, and `right`.
+        let (left, right) = {v}.split_at_mut(mid);
+        let (pivot, right) = right.split_at_mut(1);
+        let pivot = &pivot[0];
+
+        if mid < index {
+            v = right;
+            index = index - mid - 1;
+            pred = Some(pivot);
+        } else if mid > index {
+            v = left;
+        } else {
+            // If mid == index, then we're done, since partition() guaranteed that all elements
+            // after mid are greater than or equal to mid.
+            return;
+        }
+    }
+}
+
+pub fn partition_at_index<T, F>(v: &mut [T], index: usize, mut is_less: F)
+                                -> (&mut [T], &mut T, &mut [T]) where F: FnMut(&T, &T) -> bool
+{
+    use cmp::Ordering::Less;
+    use cmp::Ordering::Greater;
+
+    if index >= v.len() {
+        panic!("partition_at_index index {} greater than length of slice {}", index, v.len());
+    }
+
+    if mem::size_of::<T>() == 0 {
+        // Sorting has no meaningful behavior on zero-sized types. Do nothing.
+    } else if index == v.len() - 1 {
+        // Find max element and place it in the last position of the array. We're free to use
+        // `unwrap()` here because we know v must not be empty.
+        let (max_index, _) = v.iter().enumerate().max_by(
+            |&(_, x), &(_, y)| if is_less(x, y) { Less } else { Greater }).unwrap();
+        v.swap(max_index, index);
+    } else if index == 0 {
+        // Find min element and place it in the first position of the array. We're free to use
+        // `unwrap()` here because we know v must not be empty.
+        let (min_index, _) = v.iter().enumerate().min_by(
+            |&(_, x), &(_, y)| if is_less(x, y) { Less } else { Greater }).unwrap();
+        v.swap(min_index, index);
+    } else {
+        partition_at_index_loop(v, index, &mut is_less, None);
+    }
+
+    let (left, right) = v.split_at_mut(index);
+    let (pivot, right) = right.split_at_mut(1);
+    let pivot = &mut pivot[0];
+    (left, pivot, right)
+}

src/libcore/tests/lib.rs

@@ -21,6 +21,7 @@
 #![feature(refcell_replace_swap)]
 #![feature(slice_patterns)]
 #![feature(sort_internals)]
+#![feature(slice_partition_at_index)]
 #![feature(specialization)]
 #![feature(step_trait)]
 #![feature(str_internals)]

src/libcore/tests/slice.rs

@@ -1084,6 +1084,124 @@ fn sort_unstable() {
     assert!(v == [0xDEADBEEF]);
 }
 
+#[test]
+#[cfg(not(target_arch = "wasm32"))]
+#[cfg(not(miri))] // Miri does not support entropy
+fn partition_at_index() {
+    use core::cmp::Ordering::{Equal, Greater, Less};
+    use rand::rngs::SmallRng;
+    use rand::seq::SliceRandom;
+    use rand::{FromEntropy, Rng};
+
+    let mut rng = SmallRng::from_entropy();
+
+    for len in (2..21).chain(500..501) {
+        let mut orig = vec![0; len];
+
+        for &modulus in &[5, 10, 1000] {
+            for _ in 0..10 {
+                for i in 0..len {
+                    orig[i] = rng.gen::<i32>() % modulus;
+                }
+
+                let v_sorted = {
+                    let mut v = orig.clone();
+                    v.sort();
+                    v
+                };
+
+                // Sort in default order.
+                for pivot in 0..len {
+                    let mut v = orig.clone();
+                    v.partition_at_index(pivot);
+
+                    assert_eq!(v_sorted[pivot], v[pivot]);
+                    for i in 0..pivot {
+                        for j in pivot..len {
+                            assert!(v[i] <= v[j]);
+                        }
+                    }
+                }
+
+                // Sort in ascending order.
+                for pivot in 0..len {
+                    let mut v = orig.clone();
+                    let (left, pivot, right) = v.partition_at_index_by(pivot, |a, b| a.cmp(b));
+
+                    assert_eq!(left.len() + right.len(), len - 1);
+
+                    for l in left {
+                        assert!(l <= pivot);
+                        for r in right.iter_mut() {
+                            assert!(l <= r);
+                            assert!(pivot <= r);
+                        }
+                    }
+                }
+
+                // Sort in descending order.
+                let sort_descending_comparator = |a: &i32, b: &i32| b.cmp(a);
+                let v_sorted_descending = {
+                    let mut v = orig.clone();
+                    v.sort_by(sort_descending_comparator);
+                    v
+                };
+
+                for pivot in 0..len {
+                    let mut v = orig.clone();
+                    v.partition_at_index_by(pivot, sort_descending_comparator);
+
+                    assert_eq!(v_sorted_descending[pivot], v[pivot]);
+                    for i in 0..pivot {
+                        for j in pivot..len {
+                            assert!(v[j] <= v[i]);
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    // Sort at index using a completely random comparison function.
+    // This will reorder the elements *somehow*, but won't panic.
+    let mut v = [0; 500];
+    for i in 0..v.len() {
+        v[i] = i as i32;
+    }
+
+    for pivot in 0..v.len() {
+        v.partition_at_index_by(pivot, |_, _| *[Less, Equal, Greater].choose(&mut rng).unwrap());
+        v.sort();
+        for i in 0..v.len() {
+            assert_eq!(v[i], i as i32);
+        }
+    }
+
+    // Should not panic.
+    [(); 10].partition_at_index(0);
+    [(); 10].partition_at_index(5);
+    [(); 10].partition_at_index(9);
+    [(); 100].partition_at_index(0);
+    [(); 100].partition_at_index(50);
+    [(); 100].partition_at_index(99);
+
+    let mut v = [0xDEADBEEFu64];
+    v.partition_at_index(0);
+    assert!(v == [0xDEADBEEF]);
+}
+
+#[test]
+#[should_panic(expected = "index 0 greater than length of slice")]
+fn partition_at_index_zero_length() {
+    [0i32; 0].partition_at_index(0);
+}
+
+#[test]
+#[should_panic(expected = "index 20 greater than length of slice")]
+fn partition_at_index_past_length() {
+    [0i32; 10].partition_at_index(20);
+}
+
 pub mod memchr {
     use core::slice::memchr::{memchr, memrchr};