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use std::ptr;
use crate::data_types::Latent;
pub fn choose_pivot<L: Latent>(latents: &[L]) -> L {
// Minimum length to choose the median-of-medians method.
// Shorter slices use the simple median-of-three method.
const SHORTEST_MEDIAN_OF_MEDIANS: usize = 50;
let len = latents.len();
// Three indices near which we are going to choose a pivot.
let mut a = len / 4;
let mut b = len / 2;
let mut c = (len * 3) / 4;
if len >= 8 {
// Swaps indices so that `v[a] <= v[b]`.
// SAFETY: `len >= 8` so there are at least two elements in the neighborhoods of
// `a`, `b` and `c`. This means the three calls to `sort_adjacent` result in
// corresponding calls to `sort3` with valid 3-item neighborhoods around each
// pointer, which in turn means the calls to `sort2` are done with valid
// references. Thus the `v.get_unchecked` calls are safe, as is the `ptr::swap`
// call.
let sort2 = |a: &mut usize, b: &mut usize| unsafe {
if *latents.get_unchecked(*b) < *latents.get_unchecked(*a) {
ptr::swap(a, b);
}
};
// Swaps indices so that `v[a] <= v[b] <= v[c]`.
let sort3 = |a: &mut usize, b: &mut usize, c: &mut usize| {
sort2(a, b);
sort2(b, c);
sort2(a, b);
};
if len >= SHORTEST_MEDIAN_OF_MEDIANS {
// Finds the median of `v[a - 1], v[a], v[a + 1]` and stores the index into `a`.
let sort_adjacent = |a: &mut usize| {
let tmp = *a;
sort3(&mut (tmp - 1), a, &mut (tmp + 1));
};
// Find medians in the neighborhoods of `a`, `b`, and `c`.
sort_adjacent(&mut a);
sort_adjacent(&mut b);
sort_adjacent(&mut c);
}
// Find the median among `a`, `b`, and `c`.
sort3(&mut a, &mut b, &mut c);
}
latents[b]
}
// Scatters some elements around in an attempt to break patterns that might cause imbalanced
// partitions in quicksort.
#[cold]
pub fn break_patterns<L>(v: &mut [L]) {
let len = v.len();
if len >= 8 {
let mut seed = len;
let mut gen_usize = || {
// Pseudorandom number generator from the "Xorshift RNGs" paper by George Marsaglia.
if usize::BITS <= 32 {
let mut r = seed as u32;
r ^= r << 13;
r ^= r >> 17;
r ^= r << 5;
seed = r as usize;
seed
} else {
let mut r = seed as u64;
r ^= r << 13;
r ^= r >> 7;
r ^= r << 17;
seed = r as usize;
seed
}
};
// Take random numbers modulo this number.
// The number fits into `usize` because `len` is not greater than `isize::MAX`.
let modulus = len.next_power_of_two();
// Some pivot candidates will be in the nearby of this index. Let's randomize them.
let pos = len / 4 * 2;
for i in 0..3 {
// Generate a random number modulo `len`. However, in order to avoid costly operations
// we first take it modulo a power of two, and then decrease by `len` until it fits
// into the range `[0, len - 1]`.
let mut other = gen_usize() & (modulus - 1);
// `other` is guaranteed to be less than `2 * len`.
if other >= len {
other -= len;
}
v.swap(pos - 1 + i, other);
}
}
}
// returns (count on left side of pivot, was_bad_pivot)
// Uses lomuto partitioning
pub fn partition<L: Latent>(latents: &mut [L], pivot: L) -> (usize, bool) {
// |-- < pivot--|-- >= pivot --|-- unprocessed --|
let mut left_idx = 0;
let mut pos = latents.as_mut_ptr();
unsafe {
let end = latents.as_mut_ptr().add(latents.len());
while pos < end {
let value = *pos;
let is_lt_pivot = value < pivot;
*pos = *latents.get_unchecked(left_idx);
*latents.get_unchecked_mut(left_idx) = value;
left_idx += is_lt_pivot as usize;
pos = pos.add(1);
}
}
let was_bad_pivot = 1 + left_idx.min(latents.len() - left_idx) < latents.len() / 8;
(left_idx, was_bad_pivot)
}
// Sorts `v` using heapsort, which guarantees *O*(*n* \* log(*n*)) worst-case.
#[cold]
pub fn heapsort<L: Latent>(latents: &mut [L]) {
// This binary heap respects the invariant `parent >= child`.
let sift_down = |x: &mut [L], mut node| {
loop {
// Children of `node`.
let mut child = 2 * node + 1;
if child >= x.len() {
break;
}
// Choose the greater child.
if child + 1 < x.len() {
// We need a branch to be sure not to out-of-bounds index,
// but it's highly predictable. The comparison, however,
// is better done branchless, especially for primitives.
child += (x[child] < x[child + 1]) as usize;
}
// Stop if the invariant holds at `node`.
if x[node] >= x[child] {
break;
}
// Swap `node` with the greater child, move one step down, and continue sifting.
x.swap(node, child);
node = child;
}
};
// Build the heap in linear time.
for i in (0..latents.len() / 2).rev() {
sift_down(latents, i);
}
// Pop maximal elements from the heap.
for i in (1..latents.len()).rev() {
latents.swap(0, i);
sift_down(&mut latents[..i], 0);
}
}