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Diffstat (limited to 'library/core/src/slice/rotate.rs')
| -rw-r--r-- | library/core/src/slice/rotate.rs | 234 |
1 files changed, 234 insertions, 0 deletions
diff --git a/library/core/src/slice/rotate.rs b/library/core/src/slice/rotate.rs new file mode 100644 index 000000000..4589c6c0f --- /dev/null +++ b/library/core/src/slice/rotate.rs @@ -0,0 +1,234 @@ +use crate::cmp; +use crate::mem::{self, MaybeUninit}; +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 mem::size_of::<T>() == 0 { + 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; + } + } + } + } +} |