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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 : 44 : static bool is_aligned(const void *base, size_t size, unsigned char align)
34 : : {
35 : 44 : unsigned char lsbits = (unsigned char)size;
36 : :
37 : 44 : (void)base;
38 : : #ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS
39 : : lsbits |= (unsigned char)(uintptr_t)base;
40 : : #endif
41 : 44 : 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 stil 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 : 0 : 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 : 1243 : do {
86 : : #ifdef CONFIG_64BIT
87 : 1243 : u64 t = *(u64 *)(a + (n -= 8));
88 : 1243 : *(u64 *)(a + n) = *(u64 *)(b + n);
89 : 1243 : *(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 [ + + ]: 1243 : } 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 : 0 : 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_func_t)0
126 : : #define SWAP_WORDS_32 (swap_func_t)1
127 : : #define SWAP_BYTES (swap_func_t)2
128 : :
129 : : /*
130 : : * The function pointer is last to make tail calls most efficient if the
131 : : * compiler decides not to inline this function.
132 : : */
133 : 537383 : static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func)
134 : : {
135 [ + + ]: 537383 : if (swap_func == SWAP_WORDS_64)
136 : : swap_words_64(a, b, size);
137 [ - + ]: 536184 : else if (swap_func == SWAP_WORDS_32)
138 : : swap_words_32(a, b, size);
139 [ - + ]: 536184 : else if (swap_func == SWAP_BYTES)
140 : : swap_bytes(a, b, size);
141 : : else
142 : 536184 : swap_func(a, b, (int)size);
143 : 537383 : }
144 : :
145 : : #define _CMP_WRAPPER ((cmp_r_func_t)0L)
146 : :
147 : 593241 : static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)
148 : : {
149 : 593241 : if (cmp == _CMP_WRAPPER)
150 : 593241 : return ((cmp_func_t)(priv))(a, b);
151 : 0 : return cmp(a, b, priv);
152 : : }
153 : :
154 : : /**
155 : : * parent - given the offset of the child, find the offset of the parent.
156 : : * @i: the offset of the heap element whose parent is sought. Non-zero.
157 : : * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
158 : : * @size: size of each element
159 : : *
160 : : * In terms of array indexes, the parent of element j = @i/@size is simply
161 : : * (j-1)/2. But when working in byte offsets, we can't use implicit
162 : : * truncation of integer divides.
163 : : *
164 : : * Fortunately, we only need one bit of the quotient, not the full divide.
165 : : * @size has a least significant bit. That bit will be clear if @i is
166 : : * an even multiple of @size, and set if it's an odd multiple.
167 : : *
168 : : * Logically, we're doing "if (i & lsbit) i -= size;", but since the
169 : : * branch is unpredictable, it's done with a bit of clever branch-free
170 : : * code instead.
171 : : */
172 : : __attribute_const__ __always_inline
173 : 503305 : static size_t parent(size_t i, unsigned int lsbit, size_t size)
174 : : {
175 : 503305 : i -= size;
176 : 503305 : i -= size & -(i & lsbit);
177 : 503305 : return i / 2;
178 : : }
179 : :
180 : : /**
181 : : * sort_r - sort an array of elements
182 : : * @base: pointer to data to sort
183 : : * @num: number of elements
184 : : * @size: size of each element
185 : : * @cmp_func: pointer to comparison function
186 : : * @swap_func: pointer to swap function or NULL
187 : : * @priv: third argument passed to comparison function
188 : : *
189 : : * This function does a heapsort on the given array. You may provide
190 : : * a swap_func function if you need to do something more than a memory
191 : : * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
192 : : * avoids a slow retpoline and so is significantly faster.
193 : : *
194 : : * Sorting time is O(n log n) both on average and worst-case. While
195 : : * quicksort is slightly faster on average, it suffers from exploitable
196 : : * O(n*n) worst-case behavior and extra memory requirements that make
197 : : * it less suitable for kernel use.
198 : : */
199 : 154 : void sort_r(void *base, size_t num, size_t size,
200 : : cmp_r_func_t cmp_func,
201 : : swap_func_t swap_func,
202 : : const void *priv)
203 : : {
204 : : /* pre-scale counters for performance */
205 : 154 : size_t n = num * size, a = (num/2) * size;
206 : 154 : const unsigned int lsbit = size & -size; /* Used to find parent */
207 : :
208 [ + + ]: 154 : if (!a) /* num < 2 || size == 0 */
209 : : return;
210 : :
211 [ + + ]: 66 : if (!swap_func) {
212 [ - + ]: 44 : if (is_aligned(base, size, 8))
213 : : swap_func = SWAP_WORDS_64;
214 [ # # ]: 0 : else if (is_aligned(base, size, 4))
215 : : swap_func = SWAP_WORDS_32;
216 : : else
217 : 0 : swap_func = SWAP_BYTES;
218 : : }
219 : :
220 : : /*
221 : : * Loop invariants:
222 : : * 1. elements [a,n) satisfy the heap property (compare greater than
223 : : * all of their children),
224 : : * 2. elements [n,num*size) are sorted, and
225 : : * 3. a <= b <= c <= d <= n (whenever they are valid).
226 : : */
227 : 78507 : for (;;) {
228 : 78507 : size_t b, c, d;
229 : :
230 [ + + ]: 78507 : if (a) /* Building heap: sift down --a */
231 : 26169 : a -= size;
232 [ + + ]: 52338 : else if (n -= size) /* Sorting: Extract root to --n */
233 : 52272 : do_swap(base, base + n, size, swap_func);
234 : : else /* Sort complete */
235 : : break;
236 : :
237 : : /*
238 : : * Sift element at "a" down into heap. This is the
239 : : * "bottom-up" variant, which significantly reduces
240 : : * calls to cmp_func(): we find the sift-down path all
241 : : * the way to the leaves (one compare per level), then
242 : : * backtrack to find where to insert the target element.
243 : : *
244 : : * Because elements tend to sift down close to the leaves,
245 : : * this uses fewer compares than doing two per level
246 : : * on the way down. (A bit more than half as many on
247 : : * average, 3/4 worst-case.)
248 : : */
249 [ + + ]: 577104 : for (b = a; c = 2*b + size, (d = c + size) < n;)
250 [ + - + + ]: 997326 : b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d;
251 [ + + ]: 78441 : if (d == n) /* Special case last leaf with no sibling */
252 : 4642 : b = c;
253 : :
254 : : /* Now backtrack from "b" to the correct location for "a" */
255 [ + + + - : 191213 : while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
+ + ]
256 : 18194 : b = parent(b, lsbit, size);
257 : 78441 : c = b; /* Where "a" belongs */
258 [ + + ]: 563552 : while (b != a) { /* Shift it into place */
259 : 485111 : b = parent(b, lsbit, size);
260 : 485111 : do_swap(base + b, base + c, size, swap_func);
261 : : }
262 : : }
263 : : }
264 : : EXPORT_SYMBOL(sort_r);
265 : :
266 : 154 : void sort(void *base, size_t num, size_t size,
267 : : cmp_func_t cmp_func,
268 : : swap_func_t swap_func)
269 : : {
270 : 154 : return sort_r(base, num, size, _CMP_WRAPPER, swap_func, cmp_func);
271 : : }
272 : : EXPORT_SYMBOL(sort);
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