rotate.rs

use crate::cmp;
use crate::mem::{self, MaybeUninit, SizedTypeProperties};
use crate::ptr;

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