183 lines
8.1 KiB
Rust
183 lines
8.1 KiB
Rust
// ignore-tidy-undocumented-unsafe
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use crate::cmp;
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use crate::mem::{self, MaybeUninit};
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use crate::ptr;
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/// Rotates the range `[mid-left, mid+right)` such that the element at `mid` becomes the first
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/// element. Equivalently, rotates the range `left` elements to the left or `right` elements to the
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/// right.
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///
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/// # Safety
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///
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/// The specified range must be valid for reading and writing.
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///
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/// # Algorithm
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///
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/// Algorithm 1 is used for small values of `left + right` or for large `T`. The elements are moved
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/// into their final positions one at a time starting at `mid - left` and advancing by `right` steps
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/// modulo `left + right`, such that only one temporary is needed. Eventually, we arrive back at
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/// `mid - left`. However, if `gcd(left + right, right)` is not 1, the above steps skipped over
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/// elements. For example:
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/// ```text
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/// left = 10, right = 6
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/// the `^` indicates an element in its final place
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/// 6 7 8 9 10 11 12 13 14 15 . 0 1 2 3 4 5
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/// after using one step of the above algorithm (The X will be overwritten at the end of the round,
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/// and 12 is stored in a temporary):
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/// X 7 8 9 10 11 6 13 14 15 . 0 1 2 3 4 5
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/// ^
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/// after using another step (now 2 is in the temporary):
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/// X 7 8 9 10 11 6 13 14 15 . 0 1 12 3 4 5
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/// ^ ^
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/// after the third step (the steps wrap around, and 8 is in the temporary):
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/// X 7 2 9 10 11 6 13 14 15 . 0 1 12 3 4 5
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/// ^ ^ ^
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/// after 7 more steps, the round ends with the temporary 0 getting put in the X:
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/// 0 7 2 9 4 11 6 13 8 15 . 10 1 12 3 14 5
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/// ^ ^ ^ ^ ^ ^ ^ ^
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/// ```
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/// Fortunately, the number of skipped over elements between finalized elements is always equal, so
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/// we can just offset our starting position and do more rounds (the total number of rounds is the
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/// `gcd(left + right, right)` value). The end result is that all elements are finalized once and
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/// only once.
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///
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/// Algorithm 2 is used if `left + right` is large but `min(left, right)` is small enough to
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/// fit onto a stack buffer. The `min(left, right)` elements are copied onto the buffer, `memmove`
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/// is applied to the others, and the ones on the buffer are moved back into the hole on the
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/// opposite side of where they originated.
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///
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/// Algorithms that can be vectorized outperform the above once `left + right` becomes large enough.
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/// Algorithm 1 can be vectorized by chunking and performing many rounds at once, but there are too
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/// few rounds on average until `left + right` is enormous, and the worst case of a single
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/// round is always there. Instead, algorithm 3 utilizes repeated swapping of
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/// `min(left, right)` elements until a smaller rotate problem is left.
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///
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/// ```text
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/// left = 11, right = 4
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/// [4 5 6 7 8 9 10 11 12 13 14 . 0 1 2 3]
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/// ^ ^ ^ ^ ^ ^ ^ ^ swapping the right most elements with elements to the left
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/// [4 5 6 7 8 9 10 . 0 1 2 3] 11 12 13 14
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/// ^ ^ ^ ^ ^ ^ ^ ^ swapping these
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/// [4 5 6 . 0 1 2 3] 7 8 9 10 11 12 13 14
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/// we cannot swap any more, but a smaller rotation problem is left to solve
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/// ```
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/// when `left < right` the swapping happens from the left instead.
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pub unsafe fn ptr_rotate<T>(mut left: usize, mut mid: *mut T, mut right: usize) {
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type BufType = [usize; 32];
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if mem::size_of::<T>() == 0 {
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return;
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}
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loop {
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// N.B. the below algorithms can fail if these cases are not checked
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if (right == 0) || (left == 0) {
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return;
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}
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if (left + right < 24) || (mem::size_of::<T>() > mem::size_of::<[usize; 4]>()) {
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// Algorithm 1
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// Microbenchmarks indicate that the average performance for random shifts is better all
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// the way until about `left + right == 32`, but the worst case performance breaks even
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// around 16. 24 was chosen as middle ground. If the size of `T` is larger than 4
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// `usize`s, this algorithm also outperforms other algorithms.
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let x = unsafe { mid.sub(left) };
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// beginning of first round
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let mut tmp: T = unsafe { x.read() };
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let mut i = right;
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// `gcd` can be found before hand by calculating `gcd(left + right, right)`,
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// but it is faster to do one loop which calculates the gcd as a side effect, then
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// doing the rest of the chunk
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let mut gcd = right;
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// benchmarks reveal that it is faster to swap temporaries all the way through instead
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// of reading one temporary once, copying backwards, and then writing that temporary at
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// the very end. This is possibly due to the fact that swapping or replacing temporaries
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// uses only one memory address in the loop instead of needing to manage two.
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loop {
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tmp = unsafe { x.add(i).replace(tmp) };
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// instead of incrementing `i` and then checking if it is outside the bounds, we
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// check if `i` will go outside the bounds on the next increment. This prevents
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// any wrapping of pointers or `usize`.
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if i >= left {
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i -= left;
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if i == 0 {
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// end of first round
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unsafe { x.write(tmp) };
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break;
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}
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// this conditional must be here if `left + right >= 15`
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if i < gcd {
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gcd = i;
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}
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} else {
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i += right;
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}
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}
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// finish the chunk with more rounds
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for start in 1..gcd {
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tmp = unsafe { x.add(start).read() };
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i = start + right;
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loop {
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tmp = unsafe { x.add(i).replace(tmp) };
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if i >= left {
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i -= left;
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if i == start {
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unsafe { x.add(start).write(tmp) };
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break;
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}
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} else {
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i += right;
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}
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}
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}
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return;
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// `T` is not a zero-sized type, so it's okay to divide by its size.
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} else if cmp::min(left, right) <= mem::size_of::<BufType>() / mem::size_of::<T>() {
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// Algorithm 2
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// The `[T; 0]` here is to ensure this is appropriately aligned for T
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let mut rawarray = MaybeUninit::<(BufType, [T; 0])>::uninit();
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let buf = rawarray.as_mut_ptr() as *mut T;
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let dim = unsafe { mid.sub(left).add(right) };
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if left <= right {
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unsafe {
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ptr::copy_nonoverlapping(mid.sub(left), buf, left);
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ptr::copy(mid, mid.sub(left), right);
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ptr::copy_nonoverlapping(buf, dim, left);
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}
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} else {
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unsafe {
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ptr::copy_nonoverlapping(mid, buf, right);
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ptr::copy(mid.sub(left), dim, left);
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ptr::copy_nonoverlapping(buf, mid.sub(left), right);
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}
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}
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return;
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} else if left >= right {
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// Algorithm 3
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// There is an alternate way of swapping that involves finding where the last swap
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// of this algorithm would be, and swapping using that last chunk instead of swapping
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// adjacent chunks like this algorithm is doing, but this way is still faster.
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loop {
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unsafe {
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ptr::swap_nonoverlapping(mid.sub(right), mid, right);
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mid = mid.sub(right);
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}
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left -= right;
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if left < right {
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break;
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}
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}
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} else {
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// Algorithm 3, `left < right`
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loop {
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unsafe {
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ptr::swap_nonoverlapping(mid.sub(left), mid, left);
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mid = mid.add(left);
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}
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right -= left;
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if right < left {
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break;
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}
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}
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}
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}
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}
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