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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 * Quicksort 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 <linux/types.h>
14#include <linux/export.h>
15#include <linux/sort.h>
16
17/**
18 * is_aligned - is this pointer & size okay for word-wide copying?
19 * @base: pointer to data
20 * @size: size of each element
21 * @align: required alignment (typically 4 or 8)
22 *
23 * Returns true if elements can be copied using word loads and stores.
24 * The size must be a multiple of the alignment, and the base address must
25 * be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS.
26 *
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.
29 */
30__attribute_const__ __always_inline
31static bool is_aligned(const void *base, size_t size, unsigned char align)
32{
33 unsigned char lsbits = (unsigned char)size;
34
35 (void)base;
36#ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS
37 lsbits |= (unsigned char)(uintptr_t)base;
38#endif
39 return (lsbits & (align - 1)) == 0;
40}
41
42/**
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)
47 *
48 * Exchange the two objects in memory. This exploits base+index addressing,
49 * which basically all CPUs have, to minimize loop overhead computations.
50 *
51 * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
52 * bottom of the loop, even though the zero flag is still valid from the
53 * subtract (since the intervening mov instructions don't alter the flags).
54 * Gcc 8.1.0 doesn't have that problem.
55 */
56static void swap_words_32(void *a, void *b, size_t n)
57{
58 do {
59 u32 t = *(u32 *)(a + (n -= 4));
60 *(u32 *)(a + n) = *(u32 *)(b + n);
61 *(u32 *)(b + n) = t;
62 } while (n);
63}
64
65/**
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)
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 */
81static void swap_words_64(void *a, void *b, size_t n)
82{
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);
99}
100
101/**
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
105 * @n: element size
106 *
107 * This is the fallback if alignment doesn't allow using larger chunks.
108 */
109static void swap_bytes(void *a, void *b, size_t n)
110{
111 do {
112 char t = ((char *)a)[--n];
113 ((char *)a)[n] = ((char *)b)[n];
114 ((char *)b)[n] = t;
115 } while (n);
116}
117
118/*
119 * The values are arbitrary as long as they can't be confused with
120 * a pointer, but small integers make for the smallest compare
121 * instructions.
122 */
123#define SWAP_WORDS_64 (swap_r_func_t)0
124#define SWAP_WORDS_32 (swap_r_func_t)1
125#define SWAP_BYTES (swap_r_func_t)2
126#define SWAP_WRAPPER (swap_r_func_t)3
127
128struct wrapper {
129 cmp_func_t cmp;
130 swap_func_t swap;
131};
132
133/*
134 * The function pointer is last to make tail calls most efficient if the
135 * compiler decides not to inline this function.
136 */
137static void do_swap(void *a, void *b, size_t size, swap_r_func_t swap_func, const void *priv)
138{
139 if (swap_func == SWAP_WRAPPER) {
140 ((const struct wrapper *)priv)->swap(a, b, (int)size);
141 return;
142 }
143
144 if (swap_func == SWAP_WORDS_64)
145 swap_words_64(a, b, size);
146 else if (swap_func == SWAP_WORDS_32)
147 swap_words_32(a, b, size);
148 else if (swap_func == SWAP_BYTES)
149 swap_bytes(a, b, size);
150 else
151 swap_func(a, b, (int)size, priv);
152}
153
154#define _CMP_WRAPPER ((cmp_r_func_t)0L)
155
156static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)
157{
158 if (cmp == _CMP_WRAPPER)
159 return ((const struct wrapper *)priv)->cmp(a, b);
160 return cmp(a, b, priv);
161}
162
163/**
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"
167 * @size: size of each element
168 *
169 * In terms of array indexes, the parent of element j = @i/@size is simply
170 * (j-1)/2. But when working in byte offsets, we can't use implicit
171 * truncation of integer divides.
172 *
173 * Fortunately, we only need one bit of the quotient, not the full divide.
174 * @size has a least significant bit. That bit will be clear if @i is
175 * an even multiple of @size, and set if it's an odd multiple.
176 *
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
179 * code instead.
180 */
181__attribute_const__ __always_inline
182static size_t parent(size_t i, unsigned int lsbit, size_t size)
183{
184 i -= size;
185 i -= size & -(i & lsbit);
186 return i / 2;
187}
188
189#include <linux/sched.h>
190
191static void __sort_r(void *base, size_t num, size_t size,
192 cmp_r_func_t cmp_func,
193 swap_r_func_t swap_func,
194 const void *priv,
195 bool may_schedule)
196{
197 /* pre-scale counters for performance */
198 size_t n = num * size, a = (num/2) * size;
199 const unsigned int lsbit = size & -size; /* Used to find parent */
200 size_t shift = 0;
201
202 if (!a) /* num < 2 || size == 0 */
203 return;
204
205 /* called from 'sort' without swap function, let's pick the default */
206 if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
207 swap_func = NULL;
208
209 if (!swap_func) {
210 if (is_aligned(base, size, 8))
211 swap_func = SWAP_WORDS_64;
212 else if (is_aligned(base, size, 4))
213 swap_func = SWAP_WORDS_32;
214 else
215 swap_func = SWAP_BYTES;
216 }
217
218 /*
219 * Loop invariants:
220 * 1. elements [a,n) satisfy the heap property (compare greater than
221 * all of their children),
222 * 2. elements [n,num*size) are sorted, and
223 * 3. a <= b <= c <= d <= n (whenever they are valid).
224 */
225 for (;;) {
226 size_t b, c, d;
227
228 if (a) /* Building heap: sift down a */
229 a -= size << shift;
230 else if (n > 3 * size) { /* Sorting: Extract two largest elements */
231 n -= size;
232 do_swap(base, base + n, size, swap_func, priv);
233 shift = do_cmp(base + size, base + 2 * size, cmp_func, priv) <= 0;
234 a = size << shift;
235 n -= size;
236 do_swap(base + a, base + n, size, swap_func, priv);
237 } else { /* Sort complete */
238 break;
239 }
240
241 /*
242 * Sift element at "a" down into heap. This is the
243 * "bottom-up" variant, which significantly reduces
244 * calls to cmp_func(): we find the sift-down path all
245 * the way to the leaves (one compare per level), then
246 * backtrack to find where to insert the target element.
247 *
248 * Because elements tend to sift down close to the leaves,
249 * this uses fewer compares than doing two per level
250 * on the way down. (A bit more than half as many on
251 * average, 3/4 worst-case.)
252 */
253 for (b = a; c = 2*b + size, (d = c + size) < n;)
254 b = do_cmp(base + c, base + d, cmp_func, priv) > 0 ? c : d;
255 if (d == n) /* Special case last leaf with no sibling */
256 b = c;
257
258 /* Now backtrack from "b" to the correct location for "a" */
259 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
260 b = parent(b, lsbit, size);
261 c = b; /* Where "a" belongs */
262 while (b != a) { /* Shift it into place */
263 b = parent(b, lsbit, size);
264 do_swap(base + b, base + c, size, swap_func, priv);
265 }
266
267 if (may_schedule)
268 cond_resched();
269 }
270
271 n -= size;
272 do_swap(base, base + n, size, swap_func, priv);
273 if (n == size * 2 && do_cmp(base, base + size, cmp_func, priv) > 0)
274 do_swap(base, base + size, size, swap_func, priv);
275}
276
277/**
278 * sort_r - sort an array of elements
279 * @base: pointer to data to sort
280 * @num: number of elements
281 * @size: size of each element
282 * @cmp_func: pointer to comparison function
283 * @swap_func: pointer to swap function or NULL
284 * @priv: third argument passed to comparison function
285 *
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.
290 *
291 * The comparison function must adhere to specific mathematical
292 * properties to ensure correct and stable sorting:
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.
297 *
298 * Sorting time is O(n log n) both on average and worst-case. While
299 * quicksort is slightly faster on average, it suffers from exploitable
300 * O(n*n) worst-case behavior and extra memory requirements that make
301 * it less suitable for kernel use.
302 */
303void sort_r(void *base, size_t num, size_t size,
304 cmp_r_func_t cmp_func,
305 swap_r_func_t swap_func,
306 const void *priv)
307{
308 __sort_r(base, num, size, cmp_func, swap_func, priv, false);
309}
310EXPORT_SYMBOL(sort_r);
311
312/**
313 * sort_r_nonatomic - sort an array of elements, with cond_resched
314 * @base: pointer to data to sort
315 * @num: number of elements
316 * @size: size of each element
317 * @cmp_func: pointer to comparison function
318 * @swap_func: pointer to swap function or NULL
319 * @priv: third argument passed to comparison function
320 *
321 * Same as sort_r, but preferred for larger arrays as it does a periodic
322 * cond_resched().
323 */
324void sort_r_nonatomic(void *base, size_t num, size_t size,
325 cmp_r_func_t cmp_func,
326 swap_r_func_t swap_func,
327 const void *priv)
328{
329 __sort_r(base, num, size, cmp_func, swap_func, priv, true);
330}
331EXPORT_SYMBOL(sort_r_nonatomic);
332
333void sort(void *base, size_t num, size_t size,
334 cmp_func_t cmp_func,
335 swap_func_t swap_func)
336{
337 struct wrapper w = {
338 .cmp = cmp_func,
339 .swap = swap_func,
340 };
341
342 return __sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w, false);
343}
344EXPORT_SYMBOL(sort);
345
346void sort_nonatomic(void *base, size_t num, size_t size,
347 cmp_func_t cmp_func,
348 swap_func_t swap_func)
349{
350 struct wrapper w = {
351 .cmp = cmp_func,
352 .swap = swap_func,
353 };
354
355 return __sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w, true);
356}
357EXPORT_SYMBOL(sort_nonatomic);