]>
Commit | Line | Data |
---|---|---|
b2441318 | 1 | // SPDX-License-Identifier: GPL-2.0 |
1da177e4 | 2 | /* |
22a241cc | 3 | * A fast, small, non-recursive O(n log n) sort for the Linux kernel |
1da177e4 | 4 | * |
22a241cc GS |
5 | * This performs n*log2(n) + 0.37*n + o(n) comparisons on average, |
6 | * and 1.5*n*log2(n) + O(n) in the (very contrived) worst case. | |
7 | * | |
8 | * Glibc qsort() manages n*log2(n) - 1.26*n for random inputs (1.63*n | |
9 | * better) at the expense of stack usage and much larger code to avoid | |
10 | * quicksort's O(n^2) worst case. | |
1da177e4 LT |
11 | */ |
12 | ||
c5adae95 KF |
13 | #define pr_fmt(fmt) KBUILD_MODNAME ": " fmt |
14 | ||
42cf8096 RV |
15 | #include <linux/types.h> |
16 | #include <linux/export.h> | |
ecec4cb7 | 17 | #include <linux/sort.h> |
1da177e4 | 18 | |
37d0ec34 GS |
19 | /** |
20 | * is_aligned - is this pointer & size okay for word-wide copying? | |
21 | * @base: pointer to data | |
22 | * @size: size of each element | |
22a241cc | 23 | * @align: required alignment (typically 4 or 8) |
37d0ec34 GS |
24 | * |
25 | * Returns true if elements can be copied using word loads and stores. | |
26 | * The size must be a multiple of the alignment, and the base address must | |
27 | * be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS. | |
28 | * | |
29 | * For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)" | |
30 | * to "if ((a | b) & mask)", so we do that by hand. | |
31 | */ | |
32 | __attribute_const__ __always_inline | |
33 | static bool is_aligned(const void *base, size_t size, unsigned char align) | |
ca96ab85 | 34 | { |
37d0ec34 GS |
35 | unsigned char lsbits = (unsigned char)size; |
36 | ||
37 | (void)base; | |
38 | #ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS | |
39 | lsbits |= (unsigned char)(uintptr_t)base; | |
40 | #endif | |
41 | return (lsbits & (align - 1)) == 0; | |
ca96ab85 DW |
42 | } |
43 | ||
37d0ec34 GS |
44 | /** |
45 | * swap_words_32 - swap two elements in 32-bit chunks | |
46 | * @a, @b: pointers to the elements | |
47 | * @size: element size (must be a multiple of 4) | |
48 | * | |
49 | * Exchange the two objects in memory. This exploits base+index addressing, | |
50 | * which basically all CPUs have, to minimize loop overhead computations. | |
51 | * | |
52 | * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the | |
53 | * bottom of the loop, even though the zero flag is stil valid from the | |
54 | * subtract (since the intervening mov instructions don't alter the flags). | |
55 | * Gcc 8.1.0 doesn't have that problem. | |
56 | */ | |
8fb583c4 | 57 | static void swap_words_32(void *a, void *b, size_t n) |
1da177e4 | 58 | { |
37d0ec34 GS |
59 | do { |
60 | u32 t = *(u32 *)(a + (n -= 4)); | |
61 | *(u32 *)(a + n) = *(u32 *)(b + n); | |
62 | *(u32 *)(b + n) = t; | |
63 | } while (n); | |
1da177e4 LT |
64 | } |
65 | ||
37d0ec34 GS |
66 | /** |
67 | * swap_words_64 - swap two elements in 64-bit chunks | |
68 | * @a, @b: pointers to the elements | |
69 | * @size: element size (must be a multiple of 8) | |
70 | * | |
71 | * Exchange the two objects in memory. This exploits base+index | |
72 | * addressing, which basically all CPUs have, to minimize loop overhead | |
73 | * computations. | |
74 | * | |
75 | * We'd like to use 64-bit loads if possible. If they're not, emulating | |
76 | * one requires base+index+4 addressing which x86 has but most other | |
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. | |
79 | * x32 ABI). Are there any cases the kernel needs to worry about? | |
80 | */ | |
8fb583c4 | 81 | static void swap_words_64(void *a, void *b, size_t n) |
ca96ab85 | 82 | { |
37d0ec34 GS |
83 | do { |
84 | #ifdef CONFIG_64BIT | |
85 | u64 t = *(u64 *)(a + (n -= 8)); | |
86 | *(u64 *)(a + n) = *(u64 *)(b + n); | |
87 | *(u64 *)(b + n) = t; | |
88 | #else | |
89 | /* Use two 32-bit transfers to avoid base+index+4 addressing */ | |
90 | u32 t = *(u32 *)(a + (n -= 4)); | |
91 | *(u32 *)(a + n) = *(u32 *)(b + n); | |
92 | *(u32 *)(b + n) = t; | |
93 | ||
94 | t = *(u32 *)(a + (n -= 4)); | |
95 | *(u32 *)(a + n) = *(u32 *)(b + n); | |
96 | *(u32 *)(b + n) = t; | |
97 | #endif | |
98 | } while (n); | |
ca96ab85 DW |
99 | } |
100 | ||
37d0ec34 GS |
101 | /** |
102 | * swap_bytes - swap two elements a byte at a time | |
103 | * @a, @b: pointers to the elements | |
104 | * @size: element size | |
105 | * | |
106 | * This is the fallback if alignment doesn't allow using larger chunks. | |
107 | */ | |
8fb583c4 | 108 | static void swap_bytes(void *a, void *b, size_t n) |
1da177e4 | 109 | { |
1da177e4 | 110 | do { |
37d0ec34 GS |
111 | char t = ((char *)a)[--n]; |
112 | ((char *)a)[n] = ((char *)b)[n]; | |
113 | ((char *)b)[n] = t; | |
114 | } while (n); | |
1da177e4 LT |
115 | } |
116 | ||
8fb583c4 GS |
117 | typedef void (*swap_func_t)(void *a, void *b, int size); |
118 | ||
119 | /* | |
120 | * The values are arbitrary as long as they can't be confused with | |
121 | * a pointer, but small integers make for the smallest compare | |
122 | * instructions. | |
123 | */ | |
124 | #define SWAP_WORDS_64 (swap_func_t)0 | |
125 | #define SWAP_WORDS_32 (swap_func_t)1 | |
126 | #define SWAP_BYTES (swap_func_t)2 | |
127 | ||
128 | /* | |
129 | * The function pointer is last to make tail calls most efficient if the | |
130 | * compiler decides not to inline this function. | |
131 | */ | |
132 | static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func) | |
133 | { | |
134 | if (swap_func == SWAP_WORDS_64) | |
135 | swap_words_64(a, b, size); | |
136 | else if (swap_func == SWAP_WORDS_32) | |
137 | swap_words_32(a, b, size); | |
138 | else if (swap_func == SWAP_BYTES) | |
139 | swap_bytes(a, b, size); | |
140 | else | |
141 | swap_func(a, b, (int)size); | |
142 | } | |
143 | ||
22a241cc GS |
144 | /** |
145 | * parent - given the offset of the child, find the offset of the parent. | |
146 | * @i: the offset of the heap element whose parent is sought. Non-zero. | |
147 | * @lsbit: a precomputed 1-bit mask, equal to "size & -size" | |
148 | * @size: size of each element | |
149 | * | |
150 | * In terms of array indexes, the parent of element j = @i/@size is simply | |
151 | * (j-1)/2. But when working in byte offsets, we can't use implicit | |
152 | * truncation of integer divides. | |
153 | * | |
154 | * Fortunately, we only need one bit of the quotient, not the full divide. | |
155 | * @size has a least significant bit. That bit will be clear if @i is | |
156 | * an even multiple of @size, and set if it's an odd multiple. | |
157 | * | |
158 | * Logically, we're doing "if (i & lsbit) i -= size;", but since the | |
159 | * branch is unpredictable, it's done with a bit of clever branch-free | |
160 | * code instead. | |
161 | */ | |
162 | __attribute_const__ __always_inline | |
163 | static size_t parent(size_t i, unsigned int lsbit, size_t size) | |
164 | { | |
165 | i -= size; | |
166 | i -= size & -(i & lsbit); | |
167 | return i / 2; | |
168 | } | |
169 | ||
72fd4a35 | 170 | /** |
1da177e4 LT |
171 | * sort - sort an array of elements |
172 | * @base: pointer to data to sort | |
173 | * @num: number of elements | |
174 | * @size: size of each element | |
b53907c0 WF |
175 | * @cmp_func: pointer to comparison function |
176 | * @swap_func: pointer to swap function or NULL | |
1da177e4 | 177 | * |
37d0ec34 GS |
178 | * This function does a heapsort on the given array. You may provide |
179 | * a swap_func function if you need to do something more than a memory | |
180 | * copy (e.g. fix up pointers or auxiliary data), but the built-in swap | |
8fb583c4 | 181 | * avoids a slow retpoline and so is significantly faster. |
1da177e4 LT |
182 | * |
183 | * Sorting time is O(n log n) both on average and worst-case. While | |
22a241cc | 184 | * quicksort is slightly faster on average, it suffers from exploitable |
1da177e4 LT |
185 | * O(n*n) worst-case behavior and extra memory requirements that make |
186 | * it less suitable for kernel use. | |
187 | */ | |
1da177e4 | 188 | void sort(void *base, size_t num, size_t size, |
b53907c0 WF |
189 | int (*cmp_func)(const void *, const void *), |
190 | void (*swap_func)(void *, void *, int size)) | |
1da177e4 LT |
191 | { |
192 | /* pre-scale counters for performance */ | |
22a241cc GS |
193 | size_t n = num * size, a = (num/2) * size; |
194 | const unsigned int lsbit = size & -size; /* Used to find parent */ | |
195 | ||
196 | if (!a) /* num < 2 || size == 0 */ | |
197 | return; | |
1da177e4 | 198 | |
ca96ab85 | 199 | if (!swap_func) { |
37d0ec34 | 200 | if (is_aligned(base, size, 8)) |
8fb583c4 | 201 | swap_func = SWAP_WORDS_64; |
37d0ec34 | 202 | else if (is_aligned(base, size, 4)) |
8fb583c4 | 203 | swap_func = SWAP_WORDS_32; |
ca96ab85 | 204 | else |
8fb583c4 | 205 | swap_func = SWAP_BYTES; |
ca96ab85 | 206 | } |
1da177e4 | 207 | |
22a241cc GS |
208 | /* |
209 | * Loop invariants: | |
210 | * 1. elements [a,n) satisfy the heap property (compare greater than | |
211 | * all of their children), | |
212 | * 2. elements [n,num*size) are sorted, and | |
213 | * 3. a <= b <= c <= d <= n (whenever they are valid). | |
214 | */ | |
215 | for (;;) { | |
216 | size_t b, c, d; | |
217 | ||
218 | if (a) /* Building heap: sift down --a */ | |
219 | a -= size; | |
220 | else if (n -= size) /* Sorting: Extract root to --n */ | |
8fb583c4 | 221 | do_swap(base, base + n, size, swap_func); |
22a241cc GS |
222 | else /* Sort complete */ |
223 | break; | |
224 | ||
225 | /* | |
226 | * Sift element at "a" down into heap. This is the | |
227 | * "bottom-up" variant, which significantly reduces | |
228 | * calls to cmp_func(): we find the sift-down path all | |
229 | * the way to the leaves (one compare per level), then | |
230 | * backtrack to find where to insert the target element. | |
231 | * | |
232 | * Because elements tend to sift down close to the leaves, | |
233 | * this uses fewer compares than doing two per level | |
234 | * on the way down. (A bit more than half as many on | |
235 | * average, 3/4 worst-case.) | |
236 | */ | |
237 | for (b = a; c = 2*b + size, (d = c + size) < n;) | |
238 | b = cmp_func(base + c, base + d) >= 0 ? c : d; | |
239 | if (d == n) /* Special case last leaf with no sibling */ | |
240 | b = c; | |
241 | ||
242 | /* Now backtrack from "b" to the correct location for "a" */ | |
243 | while (b != a && cmp_func(base + a, base + b) >= 0) | |
244 | b = parent(b, lsbit, size); | |
245 | c = b; /* Where "a" belongs */ | |
246 | while (b != a) { /* Shift it into place */ | |
247 | b = parent(b, lsbit, size); | |
8fb583c4 | 248 | do_swap(base + b, base + c, size, swap_func); |
1da177e4 LT |
249 | } |
250 | } | |
251 | } | |
1da177e4 | 252 | EXPORT_SYMBOL(sort); |