Line data Source code
1 : // SPDX-License-Identifier: GPL-2.0
2 : /*
3 : * A fast, small, non-recursive O(n log n) sort for the Linux kernel
4 : *
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.
11 : */
12 :
13 : #define pr_fmt(fmt) KBUILD_MODNAME ": " fmt
14 :
15 : #include <linux/types.h>
16 : #include <linux/export.h>
17 : #include <linux/sort.h>
18 :
19 : /**
20 : * is_aligned - is this pointer & size okay for word-wide copying?
21 : * @base: pointer to data
22 : * @size: size of each element
23 : * @align: required alignment (typically 4 or 8)
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)
34 : {
35 1 : unsigned char lsbits = (unsigned char)size;
36 :
37 : (void)base;
38 : #ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS
39 1 : lsbits |= (unsigned char)(uintptr_t)base;
40 : #endif
41 : return (lsbits & (align - 1)) == 0;
42 : }
43 :
44 : /**
45 : * swap_words_32 - swap two elements in 32-bit chunks
46 : * @a: pointer to the first element to swap
47 : * @b: pointer to the second element to swap
48 : * @n: element size (must be a multiple of 4)
49 : *
50 : * Exchange the two objects in memory. This exploits base+index addressing,
51 : * which basically all CPUs have, to minimize loop overhead computations.
52 : *
53 : * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
54 : * bottom of the loop, even though the zero flag is still valid from the
55 : * subtract (since the intervening mov instructions don't alter the flags).
56 : * Gcc 8.1.0 doesn't have that problem.
57 : */
58 : static void swap_words_32(void *a, void *b, size_t n)
59 : {
60 : do {
61 0 : u32 t = *(u32 *)(a + (n -= 4));
62 0 : *(u32 *)(a + n) = *(u32 *)(b + n);
63 0 : *(u32 *)(b + n) = t;
64 0 : } while (n);
65 : }
66 :
67 : /**
68 : * swap_words_64 - swap two elements in 64-bit chunks
69 : * @a: pointer to the first element to swap
70 : * @b: pointer to the second element to swap
71 : * @n: element size (must be a multiple of 8)
72 : *
73 : * Exchange the two objects in memory. This exploits base+index
74 : * addressing, which basically all CPUs have, to minimize loop overhead
75 : * computations.
76 : *
77 : * We'd like to use 64-bit loads if possible. If they're not, emulating
78 : * one requires base+index+4 addressing which x86 has but most other
79 : * processors do not. If CONFIG_64BIT, we definitely have 64-bit loads,
80 : * but it's possible to have 64-bit loads without 64-bit pointers (e.g.
81 : * x32 ABI). Are there any cases the kernel needs to worry about?
82 : */
83 : static void swap_words_64(void *a, void *b, size_t n)
84 : {
85 : do {
86 : #ifdef CONFIG_64BIT
87 62 : u64 t = *(u64 *)(a + (n -= 8));
88 62 : *(u64 *)(a + n) = *(u64 *)(b + n);
89 62 : *(u64 *)(b + n) = t;
90 : #else
91 : /* Use two 32-bit transfers to avoid base+index+4 addressing */
92 : u32 t = *(u32 *)(a + (n -= 4));
93 : *(u32 *)(a + n) = *(u32 *)(b + n);
94 : *(u32 *)(b + n) = t;
95 :
96 : t = *(u32 *)(a + (n -= 4));
97 : *(u32 *)(a + n) = *(u32 *)(b + n);
98 : *(u32 *)(b + n) = t;
99 : #endif
100 62 : } while (n);
101 : }
102 :
103 : /**
104 : * swap_bytes - swap two elements a byte at a time
105 : * @a: pointer to the first element to swap
106 : * @b: pointer to the second element to swap
107 : * @n: element size
108 : *
109 : * This is the fallback if alignment doesn't allow using larger chunks.
110 : */
111 : static void swap_bytes(void *a, void *b, size_t n)
112 : {
113 : do {
114 0 : char t = ((char *)a)[--n];
115 0 : ((char *)a)[n] = ((char *)b)[n];
116 0 : ((char *)b)[n] = t;
117 0 : } while (n);
118 : }
119 :
120 : /*
121 : * The values are arbitrary as long as they can't be confused with
122 : * a pointer, but small integers make for the smallest compare
123 : * instructions.
124 : */
125 : #define SWAP_WORDS_64 (swap_r_func_t)0
126 : #define SWAP_WORDS_32 (swap_r_func_t)1
127 : #define SWAP_BYTES (swap_r_func_t)2
128 : #define SWAP_WRAPPER (swap_r_func_t)3
129 :
130 : struct wrapper {
131 : cmp_func_t cmp;
132 : swap_func_t swap;
133 : };
134 :
135 : /*
136 : * The function pointer is last to make tail calls most efficient if the
137 : * compiler decides not to inline this function.
138 : */
139 31 : static void do_swap(void *a, void *b, size_t size, swap_r_func_t swap_func, const void *priv)
140 : {
141 31 : if (swap_func == SWAP_WRAPPER) {
142 0 : ((const struct wrapper *)priv)->swap(a, b, (int)size);
143 0 : return;
144 : }
145 :
146 31 : if (swap_func == SWAP_WORDS_64)
147 : swap_words_64(a, b, size);
148 0 : else if (swap_func == SWAP_WORDS_32)
149 : swap_words_32(a, b, size);
150 0 : else if (swap_func == SWAP_BYTES)
151 : swap_bytes(a, b, size);
152 : else
153 0 : swap_func(a, b, (int)size, priv);
154 : }
155 :
156 : #define _CMP_WRAPPER ((cmp_r_func_t)0L)
157 :
158 : static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)
159 : {
160 31 : if (cmp == _CMP_WRAPPER)
161 31 : return ((const struct wrapper *)priv)->cmp(a, b);
162 0 : return cmp(a, b, priv);
163 : }
164 :
165 : /**
166 : * parent - given the offset of the child, find the offset of the parent.
167 : * @i: the offset of the heap element whose parent is sought. Non-zero.
168 : * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
169 : * @size: size of each element
170 : *
171 : * In terms of array indexes, the parent of element j = @i/@size is simply
172 : * (j-1)/2. But when working in byte offsets, we can't use implicit
173 : * truncation of integer divides.
174 : *
175 : * Fortunately, we only need one bit of the quotient, not the full divide.
176 : * @size has a least significant bit. That bit will be clear if @i is
177 : * an even multiple of @size, and set if it's an odd multiple.
178 : *
179 : * Logically, we're doing "if (i & lsbit) i -= size;", but since the
180 : * branch is unpredictable, it's done with a bit of clever branch-free
181 : * code instead.
182 : */
183 : __attribute_const__ __always_inline
184 : static size_t parent(size_t i, unsigned int lsbit, size_t size)
185 : {
186 22 : i -= size;
187 22 : i -= size & -(i & lsbit);
188 22 : return i / 2;
189 : }
190 :
191 : /**
192 : * sort_r - sort an array of elements
193 : * @base: pointer to data to sort
194 : * @num: number of elements
195 : * @size: size of each element
196 : * @cmp_func: pointer to comparison function
197 : * @swap_func: pointer to swap function or NULL
198 : * @priv: third argument passed to comparison function
199 : *
200 : * This function does a heapsort on the given array. You may provide
201 : * a swap_func function if you need to do something more than a memory
202 : * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
203 : * avoids a slow retpoline and so is significantly faster.
204 : *
205 : * Sorting time is O(n log n) both on average and worst-case. While
206 : * quicksort is slightly faster on average, it suffers from exploitable
207 : * O(n*n) worst-case behavior and extra memory requirements that make
208 : * it less suitable for kernel use.
209 : */
210 1 : void sort_r(void *base, size_t num, size_t size,
211 : cmp_r_func_t cmp_func,
212 : swap_r_func_t swap_func,
213 : const void *priv)
214 : {
215 : /* pre-scale counters for performance */
216 1 : size_t n = num * size, a = (num/2) * size;
217 1 : const unsigned int lsbit = size & -size; /* Used to find parent */
218 :
219 1 : if (!a) /* num < 2 || size == 0 */
220 : return;
221 :
222 : /* called from 'sort' without swap function, let's pick the default */
223 1 : if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
224 1 : swap_func = NULL;
225 :
226 1 : if (!swap_func) {
227 1 : if (is_aligned(base, size, 8))
228 : swap_func = SWAP_WORDS_64;
229 0 : else if (is_aligned(base, size, 4))
230 : swap_func = SWAP_WORDS_32;
231 : else
232 0 : swap_func = SWAP_BYTES;
233 : }
234 :
235 : /*
236 : * Loop invariants:
237 : * 1. elements [a,n) satisfy the heap property (compare greater than
238 : * all of their children),
239 : * 2. elements [n,num*size) are sorted, and
240 : * 3. a <= b <= c <= d <= n (whenever they are valid).
241 : */
242 : for (;;) {
243 : size_t b, c, d;
244 :
245 15 : if (a) /* Building heap: sift down --a */
246 5 : a -= size;
247 10 : else if (n -= size) /* Sorting: Extract root to --n */
248 9 : do_swap(base, base + n, size, swap_func, priv);
249 : else /* Sort complete */
250 : break;
251 :
252 : /*
253 : * Sift element at "a" down into heap. This is the
254 : * "bottom-up" variant, which significantly reduces
255 : * calls to cmp_func(): we find the sift-down path all
256 : * the way to the leaves (one compare per level), then
257 : * backtrack to find where to insert the target element.
258 : *
259 : * Because elements tend to sift down close to the leaves,
260 : * this uses fewer compares than doing two per level
261 : * on the way down. (A bit more than half as many on
262 : * average, 3/4 worst-case.)
263 : */
264 46 : for (b = a; c = 2*b + size, (d = c + size) < n;)
265 36 : b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d;
266 14 : if (d == n) /* Special case last leaf with no sibling */
267 4 : b = c;
268 :
269 : /* Now backtrack from "b" to the correct location for "a" */
270 27 : while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
271 0 : b = parent(b, lsbit, size);
272 : c = b; /* Where "a" belongs */
273 36 : while (b != a) { /* Shift it into place */
274 22 : b = parent(b, lsbit, size);
275 22 : do_swap(base + b, base + c, size, swap_func, priv);
276 : }
277 : }
278 : }
279 : EXPORT_SYMBOL(sort_r);
280 :
281 1 : void sort(void *base, size_t num, size_t size,
282 : cmp_func_t cmp_func,
283 : swap_func_t swap_func)
284 : {
285 1 : struct wrapper w = {
286 : .cmp = cmp_func,
287 : .swap = swap_func,
288 : };
289 :
290 1 : return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
291 : }
292 : EXPORT_SYMBOL(sort);
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