1 // SPDX-License-Identifier: GPL-2.0
3  * A fast, small, non-recursive O(n log n) sort for the Linux kernel
8  * Quicksort manages n*log2(n) - 1.26*n for random inputs (1.63*n
18  * is_aligned - is this pointer & size okay for word-wide copying?
24  * The size must be a multiple of the alignment, and the base address must
27  * For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)"
28  * to "if ((a | b) & mask)", so we do that by hand.
39 	return (lsbits & (align - 1)) == 0;  in is_aligned()
43  * swap_words_32 - swap two elements in 32-bit chunks
44  * @a: pointer to the first element to swap
45  * @b: pointer to the second element to swap
46  * @n: element size (must be a multiple of 4)
51  * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
56 static void swap_words_32(void *a, void *b, size_t n)  in swap_words_32()  argument
59 		u32 t = *(u32 *)(a + (n -= 4));  in swap_words_32()
60 		*(u32 *)(a + n) = *(u32 *)(b + n);  in swap_words_32()
61 		*(u32 *)(b + n) = t;  in swap_words_32()
66  * swap_words_64 - swap two elements in 64-bit chunks
67  * @a: pointer to the first element to swap
68  * @b: pointer to the second element to swap
69  * @n: element size (must be a multiple of 8)
75  * We'd like to use 64-bit loads if possible.  If they're not, emulating
77  * processors do not.  If CONFIG_64BIT, we definitely have 64-bit loads,
78  * but it's possible to have 64-bit loads without 64-bit pointers (e.g.
81 static void swap_words_64(void *a, void *b, size_t n)  in swap_words_64()  argument
85 		u64 t = *(u64 *)(a + (n -= 8));  in swap_words_64()
86 		*(u64 *)(a + n) = *(u64 *)(b + n);  in swap_words_64()
87 		*(u64 *)(b + n) = t;  in swap_words_64()
89 		/* Use two 32-bit transfers to avoid base+index+4 addressing */  in swap_words_64()
90 		u32 t = *(u32 *)(a + (n -= 4));  in swap_words_64()
91 		*(u32 *)(a + n) = *(u32 *)(b + n);  in swap_words_64()
92 		*(u32 *)(b + n) = t;  in swap_words_64()
94 		t = *(u32 *)(a + (n -= 4));  in swap_words_64()
95 		*(u32 *)(a + n) = *(u32 *)(b + n);  in swap_words_64()
96 		*(u32 *)(b + n) = t;  in swap_words_64()
102  * swap_bytes - swap two elements a byte at a time
103  * @a: pointer to the first element to swap
104  * @b: pointer to the second element to swap
109 static void swap_bytes(void *a, void *b, size_t n)  in swap_bytes()  argument
112 		char t = ((char *)a)[--n];  in swap_bytes()
113 		((char *)a)[n] = ((char *)b)[n];  in swap_bytes()
114 		((char *)b)[n] = t;  in swap_bytes()
120  * a pointer, but small integers make for the smallest compare
137 static void do_swap(void *a, void *b, size_t size, swap_r_func_t swap_func, const void *priv)  in do_swap()  argument
140 		((const struct wrapper *)priv)->swap(a, b, (int)size);  in do_swap()
145 		swap_words_64(a, b, size);  in do_swap()
147 		swap_words_32(a, b, size);  in do_swap()
149 		swap_bytes(a, b, size);  in do_swap()
151 		swap_func(a, b, (int)size, priv);  in do_swap()
156 static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)  in do_cmp()  argument
159 		return ((const struct wrapper *)priv)->cmp(a, b);  in do_cmp()
160 	return cmp(a, b, priv);  in do_cmp()
164  * parent - given the offset of the child, find the offset of the parent.
165  * @i: the offset of the heap element whose parent is sought.  Non-zero.
166  * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
170  * (j-1)/2.  But when working in byte offsets, we can't use implicit
174  * @size has a least significant bit.  That bit will be clear if @i is
177  * Logically, we're doing "if (i & lsbit) i -= size;", but since the
178  * branch is unpredictable, it's done with a bit of clever branch-free
184 	i -= size;  in parent()
185 	i -= size & -(i & lsbit);  in parent()
197 	/* pre-scale counters for performance */  in __sort_r()
198 	size_t n = num * size, a = (num/2) * size;  in __sort_r()  local
199 	const unsigned int lsbit = size & -size;  /* Used to find parent */  in __sort_r()
202 	if (!a)		/* num < 2 || size == 0 */  in __sort_r()
206 	if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)  in __sort_r()
220 	 * 1. elements [a,n) satisfy the heap property (compare greater than  in __sort_r()
223 	 * 3. a <= b <= c <= d <= n (whenever they are valid).  in __sort_r()
226 		size_t b, c, d;  in __sort_r()  local
228 		if (a)			/* Building heap: sift down a */  in __sort_r()
229 			a -= size << shift;  in __sort_r()
231 			n -= size;  in __sort_r()
234 			a = size << shift;  in __sort_r()
235 			n -= size;  in __sort_r()
236 			do_swap(base + a, base + n, size, swap_func, priv);  in __sort_r()
242 		 * Sift element at "a" down into heap.  This is the  in __sort_r()
243 		 * "bottom-up" variant, which significantly reduces  in __sort_r()
244 		 * calls to cmp_func(): we find the sift-down path all  in __sort_r()
250 		 * on the way down.  (A bit more than half as many on  in __sort_r()
251 		 * average, 3/4 worst-case.)  in __sort_r()
253 		for (b = a; c = 2*b + size, (d = c + size) < n;)  in __sort_r()
254 			b = do_cmp(base + c, base + d, cmp_func, priv) > 0 ? c : d;  in __sort_r()
256 			b = c;  in __sort_r()
258 		/* Now backtrack from "b" to the correct location for "a" */  in __sort_r()
259 		while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)  in __sort_r()
260 			b = parent(b, lsbit, size);  in __sort_r()
261 		c = b;			/* Where "a" belongs */  in __sort_r()
262 		while (b != a) {	/* Shift it into place */  in __sort_r()
263 			b = parent(b, lsbit, size);  in __sort_r()
264 			do_swap(base + b, base + c, size, swap_func, priv);  in __sort_r()
271 	n -= size;  in __sort_r()
278  * sort_r - sort an array of elements
286  * This function does a heapsort on the given array.  You may provide
287  * a swap_func function if you need to do something more than a memory
288  * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
289  * avoids a slow retpoline and so is significantly faster.
293  * - Antisymmetry: cmp_func(a, b) must return the opposite sign of
294  * cmp_func(b, a).
295  * - Transitivity: if cmp_func(a, b) <= 0 and cmp_func(b, c) <= 0, then
296  * cmp_func(a, c) <= 0.
298  * Sorting time is O(n log n) both on average and worst-case. While
300  * O(n*n) worst-case behavior and extra memory requirements that make
313  * sort_r_nonatomic - sort an array of elements, with cond_resched
321  * Same as sort_r, but preferred for larger arrays as it does a periodic