2 use crate::mem::{self, MaybeUninit};
5 /// Rotates the range `[mid-left, mid+right)` such that the element at `mid` becomes the first
6 /// element. Equivalently, rotates the range `left` elements to the left or `right` elements to the
11 /// The specified range must be valid for reading and writing.
15 /// Algorithm 1 is used for small values of `left + right` or for large `T`. The elements are moved
16 /// into their final positions one at a time starting at `mid - left` and advancing by `right` steps
17 /// modulo `left + right`, such that only one temporary is needed. Eventually, we arrive back at
18 /// `mid - left`. However, if `gcd(left + right, right)` is not 1, the above steps skipped over
19 /// elements. For example:
21 /// left = 10, right = 6
22 /// the `^` indicates an element in its final place
23 /// 6 7 8 9 10 11 12 13 14 15 . 0 1 2 3 4 5
24 /// after using one step of the above algorithm (The X will be overwritten at the end of the round,
25 /// and 12 is stored in a temporary):
26 /// X 7 8 9 10 11 6 13 14 15 . 0 1 2 3 4 5
28 /// after using another step (now 2 is in the temporary):
29 /// X 7 8 9 10 11 6 13 14 15 . 0 1 12 3 4 5
31 /// after the third step (the steps wrap around, and 8 is in the temporary):
32 /// X 7 2 9 10 11 6 13 14 15 . 0 1 12 3 4 5
34 /// after 7 more steps, the round ends with the temporary 0 getting put in the X:
35 /// 0 7 2 9 4 11 6 13 8 15 . 10 1 12 3 14 5
38 /// Fortunately, the number of skipped over elements between finalized elements is always equal, so
39 /// we can just offset our starting position and do more rounds (the total number of rounds is the
40 /// `gcd(left + right, right)` value). The end result is that all elements are finalized once and
43 /// Algorithm 2 is used if `left + right` is large but `min(left, right)` is small enough to
44 /// fit onto a stack buffer. The `min(left, right)` elements are copied onto the buffer, `memmove`
45 /// is applied to the others, and the ones on the buffer are moved back into the hole on the
46 /// opposite side of where they originated.
48 /// Algorithms that can be vectorized outperform the above once `left + right` becomes large enough.
49 /// Algorithm 1 can be vectorized by chunking and performing many rounds at once, but there are too
50 /// few rounds on average until `left + right` is enormous, and the worst case of a single
51 /// round is always there. Instead, algorithm 3 utilizes repeated swapping of
52 /// `min(left, right)` elements until a smaller rotate problem is left.
55 /// left = 11, right = 4
56 /// [4 5 6 7 8 9 10 11 12 13 14 . 0 1 2 3]
57 /// ^ ^ ^ ^ ^ ^ ^ ^ swapping the right most elements with elements to the left
58 /// [4 5 6 7 8 9 10 . 0 1 2 3] 11 12 13 14
59 /// ^ ^ ^ ^ ^ ^ ^ ^ swapping these
60 /// [4 5 6 . 0 1 2 3] 7 8 9 10 11 12 13 14
61 /// we cannot swap any more, but a smaller rotation problem is left to solve
63 /// when `left < right` the swapping happens from the left instead.
64 pub unsafe fn ptr_rotate<T>(mut left: usize, mut mid: *mut T, mut right: usize) {
65 type BufType = [usize; 32];
66 if mem::size_of::<T>() == 0 {
70 // N.B. the below algorithms can fail if these cases are not checked
71 if (right == 0) || (left == 0) {
74 if (left + right < 24) || (mem::size_of::<T>() > mem::size_of::<[usize; 4]>()) {
76 // Microbenchmarks indicate that the average performance for random shifts is better all
77 // the way until about `left + right == 32`, but the worst case performance breaks even
78 // around 16. 24 was chosen as middle ground. If the size of `T` is larger than 4
79 // `usize`s, this algorithm also outperforms other algorithms.
80 // SAFETY: callers must ensure `mid - left` is valid for reading and writing.
81 let x = unsafe { mid.sub(left) };
82 // beginning of first round
83 // SAFETY: see previous comment.
84 let mut tmp: T = unsafe { x.read() };
86 // `gcd` can be found before hand by calculating `gcd(left + right, right)`,
87 // but it is faster to do one loop which calculates the gcd as a side effect, then
88 // doing the rest of the chunk
90 // benchmarks reveal that it is faster to swap temporaries all the way through instead
91 // of reading one temporary once, copying backwards, and then writing that temporary at
92 // the very end. This is possibly due to the fact that swapping or replacing temporaries
93 // uses only one memory address in the loop instead of needing to manage two.
96 // SAFETY: callers must ensure `[left, left+mid+right)` are all valid for reading and
99 // - `i` start with `right` so `mid-left <= x+i = x+right = mid-left+right < mid+right`
100 // - `i <= left+right-1` is always true
101 // - if `i < left`, `right` is added so `i < left+right` and on the next
102 // iteration `left` is removed from `i` so it doesn't go further
103 // - if `i >= left`, `left` is removed immediately and so it doesn't go further.
104 // - overflows cannot happen for `i` since the function's safety contract ask for
105 // `mid+right-1 = x+left+right` to be valid for writing
106 // - underflows cannot happen because `i` must be bigger or equal to `left` for
107 // a subtraction of `left` to happen.
109 // So `x+i` is valid for reading and writing if the caller respected the contract
110 tmp = unsafe { x.add(i).replace(tmp) };
111 // instead of incrementing `i` and then checking if it is outside the bounds, we
112 // check if `i` will go outside the bounds on the next increment. This prevents
113 // any wrapping of pointers or `usize`.
117 // end of first round
118 // SAFETY: tmp has been read from a valid source and x is valid for writing
119 // according to the caller.
120 unsafe { x.write(tmp) };
123 // this conditional must be here if `left + right >= 15`
131 // finish the chunk with more rounds
132 for start in 1..gcd {
133 // SAFETY: `gcd` is at most equal to `right` so all values in `1..gcd` are valid for
134 // reading and writing as per the function's safety contract, see [long-safety-expl]
136 tmp = unsafe { x.add(start).read() };
137 // [safety-expl-addition]
139 // Here `start < gcd` so `start < right` so `i < right+right`: `right` being the
140 // greatest common divisor of `(left+right, right)` means that `left = right` so
141 // `i < left+right` so `x+i = mid-left+i` is always valid for reading and writing
142 // according to the function's safety contract.
145 // SAFETY: see [long-safety-expl] and [safety-expl-addition]
146 tmp = unsafe { x.add(i).replace(tmp) };
150 // SAFETY: see [long-safety-expl] and [safety-expl-addition]
151 unsafe { x.add(start).write(tmp) };
160 // `T` is not a zero-sized type, so it's okay to divide by its size.
161 } else if cmp::min(left, right) <= mem::size_of::<BufType>() / mem::size_of::<T>() {
163 // The `[T; 0]` here is to ensure this is appropriately aligned for T
164 let mut rawarray = MaybeUninit::<(BufType, [T; 0])>::uninit();
165 let buf = rawarray.as_mut_ptr() as *mut T;
166 // SAFETY: `mid-left <= mid-left+right < mid+right`
167 let dim = unsafe { mid.sub(left).add(right) };
171 // 1) The `else if` condition about the sizes ensures `[mid-left; left]` will fit in
172 // `buf` without overflow and `buf` was created just above and so cannot be
173 // overlapped with any value of `[mid-left; left]`
174 // 2) [mid-left, mid+right) are all valid for reading and writing and we don't care
175 // about overlaps here.
176 // 3) The `if` condition about `left <= right` ensures writing `left` elements to
177 // `dim = mid-left+right` is valid because:
178 // - `buf` is valid and `left` elements were written in it in 1)
179 // - `dim+left = mid-left+right+left = mid+right` and we write `[dim, dim+left)`
182 ptr::copy_nonoverlapping(mid.sub(left), buf, left);
184 ptr::copy(mid, mid.sub(left), right);
186 ptr::copy_nonoverlapping(buf, dim, left);
189 // SAFETY: same reasoning as above but with `left` and `right` reversed
191 ptr::copy_nonoverlapping(mid, buf, right);
192 ptr::copy(mid.sub(left), dim, left);
193 ptr::copy_nonoverlapping(buf, mid.sub(left), right);
197 } else if left >= right {
199 // There is an alternate way of swapping that involves finding where the last swap
200 // of this algorithm would be, and swapping using that last chunk instead of swapping
201 // adjacent chunks like this algorithm is doing, but this way is still faster.
204 // `left >= right` so `[mid-right, mid+right)` is valid for reading and writing
205 // Subtracting `right` from `mid` each turn is counterbalanced by the addition and
208 ptr::swap_nonoverlapping(mid.sub(right), mid, right);
209 mid = mid.sub(right);
217 // Algorithm 3, `left < right`
219 // SAFETY: `[mid-left, mid+left)` is valid for reading and writing because
220 // `left < right` so `mid+left < mid+right`.
221 // Adding `left` to `mid` each turn is counterbalanced by the subtraction and check
224 ptr::swap_nonoverlapping(mid.sub(left), mid, left);