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 : #include <stdio.h>
14 : #include <stdbool.h>
15 : #include <linux/types.h>
16 :
17 : #include "sort.h"
18 : #include "linux_types.h"
19 :
20 : /**
21 : * is_aligned - is this pointer & size okay for word-wide copying?
22 : * @base: pointer to data
23 : * @size: size of each element
24 : * @align: required alignment (typically 4 or 8)
25 : *
26 : * Returns true if elements can be copied using word loads and stores.
27 : * The size must be a multiple of the alignment.
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 : __const __always_inline
33 : static bool is_aligned(const void *base, size_t size, unsigned char align)
34 : {
35 2297 : unsigned char lsbits = (unsigned char)size;
36 :
37 : (void)base;
38 : return (lsbits & (align - 1)) == 0;
39 : }
40 :
41 : /**
42 : * swap_words_32 - swap two elements in 32-bit chunks
43 : * @a: pointer to the first element to swap
44 : * @b: pointer to the second element to swap
45 : * @n: element size (must be a multiple of 4)
46 : *
47 : * Exchange the two objects in memory. This exploits base+index addressing,
48 : * which basically all CPUs have, to minimize loop overhead computations.
49 : *
50 : * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
51 : * bottom of the loop, even though the zero flag is still valid from the
52 : * subtract (since the intervening mov instructions don't alter the flags).
53 : * Gcc 8.1.0 doesn't have that problem.
54 : */
55 : static void swap_words_32(void *a, void *b, size_t n)
56 : {
57 : do {
58 0 : u32 t = *(u32 *)(a + (n -= 4));
59 0 : *(u32 *)(a + n) = *(u32 *)(b + n);
60 0 : *(u32 *)(b + n) = t;
61 0 : } while (n);
62 : }
63 :
64 : /**
65 : * swap_words_64 - swap two elements in 64-bit chunks
66 : * @a: pointer to the first element to swap
67 : * @b: pointer to the second element to swap
68 : * @n: element size (must be a multiple of 8)
69 : *
70 : * Exchange the two objects in memory. This exploits base+index
71 : * addressing, which basically all CPUs have, to minimize loop overhead
72 : * computations.
73 : *
74 : * We'd like to use 64-bit loads if possible. If they're not, emulating
75 : * one requires base+index+4 addressing which x86 has but most other
76 : * processors do not.
77 : */
78 : static void swap_words_64(void *a, void *b, size_t n)
79 : {
80 : do {
81 1957195 : u64 t = *(u64 *)(a + (n -= 8));
82 1957195 : *(u64 *)(a + n) = *(u64 *)(b + n);
83 1957195 : *(u64 *)(b + n) = t;
84 1957195 : } while (n);
85 : }
86 :
87 : /**
88 : * swap_bytes - swap two elements a byte at a time
89 : * @a: pointer to the first element to swap
90 : * @b: pointer to the second element to swap
91 : * @n: element size
92 : *
93 : * This is the fallback if alignment doesn't allow using larger chunks.
94 : */
95 : static void swap_bytes(void *a, void *b, size_t n)
96 : {
97 : do {
98 0 : char t = ((char *)a)[--n];
99 0 : ((char *)a)[n] = ((char *)b)[n];
100 0 : ((char *)b)[n] = t;
101 0 : } while (n);
102 : }
103 :
104 : /*
105 : * The values are arbitrary as long as they can't be confused with
106 : * a pointer, but small integers make for the smallest compare
107 : * instructions.
108 : */
109 : #define SWAP_WORDS_64 (swap_r_func_t)0
110 : #define SWAP_WORDS_32 (swap_r_func_t)1
111 : #define SWAP_BYTES (swap_r_func_t)2
112 : #define SWAP_WRAPPER (swap_r_func_t)3
113 :
114 : struct wrapper {
115 : cmp_func_t cmp;
116 : swap_func_t swap;
117 : };
118 :
119 : /*
120 : * The function pointer is last to make tail calls most efficient if the
121 : * compiler decides not to inline this function.
122 : */
123 1957195 : static void do_swap(void *a, void *b, size_t size, swap_r_func_t swap_func, const void *priv)
124 : {
125 1957195 : if (swap_func == SWAP_WRAPPER) {
126 0 : ((const struct wrapper *)priv)->swap(a, b, (int)size);
127 0 : return;
128 : }
129 :
130 1957195 : if (swap_func == SWAP_WORDS_64)
131 : swap_words_64(a, b, size);
132 0 : else if (swap_func == SWAP_WORDS_32)
133 : swap_words_32(a, b, size);
134 0 : else if (swap_func == SWAP_BYTES)
135 : swap_bytes(a, b, size);
136 : else
137 0 : swap_func(a, b, (int)size, priv);
138 : }
139 :
140 : #define _CMP_WRAPPER ((cmp_r_func_t)0L)
141 :
142 : static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)
143 : {
144 2983390 : if (cmp == _CMP_WRAPPER)
145 2983390 : return ((const struct wrapper *)priv)->cmp(a, b);
146 0 : return cmp(a, b, priv);
147 : }
148 :
149 : /**
150 : * parent - given the offset of the child, find the offset of the parent.
151 : * @i: the offset of the heap element whose parent is sought. Non-zero.
152 : * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
153 : * @size: size of each element
154 : *
155 : * In terms of array indexes, the parent of element j = @i/@size is simply
156 : * (j-1)/2. But when working in byte offsets, we can't use implicit
157 : * truncation of integer divides.
158 : *
159 : * Fortunately, we only need one bit of the quotient, not the full divide.
160 : * @size has a least significant bit. That bit will be clear if @i is
161 : * an even multiple of @size, and set if it's an odd multiple.
162 : *
163 : * Logically, we're doing "if (i & lsbit) i -= size;", but since the
164 : * branch is unpredictable, it's done with a bit of clever branch-free
165 : * code instead.
166 : */
167 : __const __always_inline
168 : static size_t parent(size_t i, unsigned int lsbit, size_t size)
169 : {
170 2157950 : i -= size;
171 2157950 : i -= size & -(i & lsbit);
172 2157950 : return i / 2;
173 : }
174 :
175 : /**
176 : * sort_r - sort an array of elements
177 : * @base: pointer to data to sort
178 : * @num: number of elements
179 : * @size: size of each element
180 : * @cmp_func: pointer to comparison function
181 : * @swap_func: pointer to swap function or NULL
182 : * @priv: third argument passed to comparison function
183 : *
184 : * This function does a heapsort on the given array. You may provide
185 : * a swap_func function if you need to do something more than a memory
186 : * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
187 : * avoids a slow retpoline and so is significantly faster.
188 : *
189 : * Sorting time is O(n log n) both on average and worst-case. While
190 : * quicksort is slightly faster on average, it suffers from exploitable
191 : * O(n*n) worst-case behavior and extra memory requirements that make
192 : * it less suitable for kernel use.
193 : */
194 3427 : void sort_r(void *base, size_t num, size_t size,
195 : cmp_r_func_t cmp_func,
196 : swap_r_func_t swap_func,
197 : const void *priv)
198 : {
199 : /* pre-scale counters for performance */
200 3427 : size_t n = num * size, a = (num/2) * size;
201 3427 : const unsigned int lsbit = size & -size; /* Used to find parent */
202 :
203 3427 : if (!a) /* num < 2 || size == 0 */
204 : return;
205 :
206 : /* called from 'sort' without swap function, let's pick the default */
207 2297 : if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
208 : swap_func = NULL;
209 :
210 0 : if (!swap_func) {
211 2297 : if (is_aligned(base, size, 8))
212 : swap_func = SWAP_WORDS_64;
213 0 : else if (is_aligned(base, size, 4))
214 : swap_func = SWAP_WORDS_32;
215 : else
216 0 : swap_func = SWAP_BYTES;
217 : }
218 :
219 : /*
220 : * Loop invariants:
221 : * 1. elements [a,n) satisfy the heap property (compare greater than
222 : * all of their children),
223 : * 2. elements [n,num*size) are sorted, and
224 : * 3. a <= b <= c <= d <= n (whenever they are valid).
225 : */
226 : for (;;) {
227 : size_t b, c, d;
228 :
229 513344 : if (a) /* Building heap: sift down --a */
230 170904 : a -= size;
231 342440 : else if (n -= size) /* Sorting: Extract root to --n */
232 340143 : do_swap(base, base + n, size, swap_func, priv);
233 : else /* Sort complete */
234 : break;
235 :
236 : /*
237 : * Sift element at "a" down into heap. This is the
238 : * "bottom-up" variant, which significantly reduces
239 : * calls to cmp_func(): we find the sift-down path all
240 : * the way to the leaves (one compare per level), then
241 : * backtrack to find where to insert the target element.
242 : *
243 : * Because elements tend to sift down close to the leaves,
244 : * this uses fewer compares than doing two per level
245 : * on the way down. (A bit more than half as many on
246 : * average, 3/4 worst-case.)
247 : */
248 3164389 : for (b = a; c = 2*b + size, (d = c + size) < n;)
249 4284590 : b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d;
250 511047 : if (d == n) /* Special case last leaf with no sibling */
251 15655 : b = c;
252 :
253 : /* Now backtrack from "b" to the correct location for "a" */
254 1893040 : while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
255 540898 : b = parent(b, lsbit, size);
256 511047 : c = b; /* Where "a" belongs */
257 2639146 : while (b != a) { /* Shift it into place */
258 1617052 : b = parent(b, lsbit, size);
259 1617052 : do_swap(base + b, base + c, size, swap_func, priv);
260 : }
261 : }
262 : }
263 :
264 3427 : void sort(void *base, size_t num, size_t size,
265 : cmp_func_t cmp_func,
266 : swap_func_t swap_func)
267 : {
268 3427 : struct wrapper w = {
269 : .cmp = cmp_func,
270 : .swap = swap_func,
271 : };
272 :
273 3427 : return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
274 : }
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