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
is_aligned(const void * base,size_t size,unsigned char align)33 static bool is_aligned(const void *base, size_t size, unsigned char align)
34 {
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;
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 */
swap_words_32(void * a,void * b,size_t n)58 static void swap_words_32(void *a, void *b, size_t n)
59 {
60 do {
61 u32 t = *(u32 *)(a + (n -= 4));
62 *(u32 *)(a + n) = *(u32 *)(b + n);
63 *(u32 *)(b + n) = t;
64 } 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 */
swap_words_64(void * a,void * b,size_t n)83 static void swap_words_64(void *a, void *b, size_t n)
84 {
85 do {
86 #ifdef CONFIG_64BIT
87 u64 t = *(u64 *)(a + (n -= 8));
88 *(u64 *)(a + n) = *(u64 *)(b + n);
89 *(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 } 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 */
swap_bytes(void * a,void * b,size_t n)111 static void swap_bytes(void *a, void *b, size_t n)
112 {
113 do {
114 char t = ((char *)a)[--n];
115 ((char *)a)[n] = ((char *)b)[n];
116 ((char *)b)[n] = t;
117 } 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 */
do_swap(void * a,void * b,size_t size,swap_r_func_t swap_func,const void * priv)139 static void do_swap(void *a, void *b, size_t size, swap_r_func_t swap_func, const void *priv)
140 {
141 if (swap_func == SWAP_WRAPPER) {
142 ((const struct wrapper *)priv)->swap(a, b, (int)size);
143 return;
144 }
145
146 if (swap_func == SWAP_WORDS_64)
147 swap_words_64(a, b, size);
148 else if (swap_func == SWAP_WORDS_32)
149 swap_words_32(a, b, size);
150 else if (swap_func == SWAP_BYTES)
151 swap_bytes(a, b, size);
152 else
153 swap_func(a, b, (int)size, priv);
154 }
155
156 #define _CMP_WRAPPER ((cmp_r_func_t)0L)
157
do_cmp(const void * a,const void * b,cmp_r_func_t cmp,const void * priv)158 static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)
159 {
160 if (cmp == _CMP_WRAPPER)
161 return ((const struct wrapper *)priv)->cmp(a, b);
162 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
parent(size_t i,unsigned int lsbit,size_t size)184 static size_t parent(size_t i, unsigned int lsbit, size_t size)
185 {
186 i -= size;
187 i -= size & -(i & lsbit);
188 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 */
sort_r(void * base,size_t num,size_t size,cmp_r_func_t cmp_func,swap_r_func_t swap_func,const void * priv)210 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 size_t n = num * size, a = (num/2) * size;
217 const unsigned int lsbit = size & -size; /* Used to find parent */
218 size_t shift = 0;
219
220 if (!a) /* num < 2 || size == 0 */
221 return;
222
223 /* called from 'sort' without swap function, let's pick the default */
224 if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
225 swap_func = NULL;
226
227 if (!swap_func) {
228 if (is_aligned(base, size, 8))
229 swap_func = SWAP_WORDS_64;
230 else if (is_aligned(base, size, 4))
231 swap_func = SWAP_WORDS_32;
232 else
233 swap_func = SWAP_BYTES;
234 }
235
236 /*
237 * Loop invariants:
238 * 1. elements [a,n) satisfy the heap property (compare greater than
239 * all of their children),
240 * 2. elements [n,num*size) are sorted, and
241 * 3. a <= b <= c <= d <= n (whenever they are valid).
242 */
243 for (;;) {
244 size_t b, c, d;
245
246 if (a) /* Building heap: sift down a */
247 a -= size << shift;
248 else if (n > 3 * size) { /* Sorting: Extract two largest elements */
249 n -= size;
250 do_swap(base, base + n, size, swap_func, priv);
251 shift = do_cmp(base + size, base + 2 * size, cmp_func, priv) <= 0;
252 a = size << shift;
253 n -= size;
254 do_swap(base + a, base + n, size, swap_func, priv);
255 } else if (n > size) { /* Sorting: Extract root */
256 n -= size;
257 do_swap(base, base + n, size, swap_func, priv);
258 } else { /* Sort complete */
259 break;
260 }
261
262 /*
263 * Sift element at "a" down into heap. This is the
264 * "bottom-up" variant, which significantly reduces
265 * calls to cmp_func(): we find the sift-down path all
266 * the way to the leaves (one compare per level), then
267 * backtrack to find where to insert the target element.
268 *
269 * Because elements tend to sift down close to the leaves,
270 * this uses fewer compares than doing two per level
271 * on the way down. (A bit more than half as many on
272 * average, 3/4 worst-case.)
273 */
274 for (b = a; c = 2*b + size, (d = c + size) < n;)
275 b = do_cmp(base + c, base + d, cmp_func, priv) > 0 ? c : d;
276 if (d == n) /* Special case last leaf with no sibling */
277 b = c;
278
279 /* Now backtrack from "b" to the correct location for "a" */
280 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
281 b = parent(b, lsbit, size);
282 c = b; /* Where "a" belongs */
283 while (b != a) { /* Shift it into place */
284 b = parent(b, lsbit, size);
285 do_swap(base + b, base + c, size, swap_func, priv);
286 }
287 }
288 }
289 EXPORT_SYMBOL(sort_r);
290
sort(void * base,size_t num,size_t size,cmp_func_t cmp_func,swap_func_t swap_func)291 void sort(void *base, size_t num, size_t size,
292 cmp_func_t cmp_func,
293 swap_func_t swap_func)
294 {
295 struct wrapper w = {
296 .cmp = cmp_func,
297 .swap = swap_func,
298 };
299
300 return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
301 }
302 EXPORT_SYMBOL(sort);
303