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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
33static 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 */
58static 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 */
83static 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 */
111static 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
130struct 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 */
139static 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
158static 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
184static 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 */
210void 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
219 if (!a) /* num < 2 || size == 0 */
220 return;
221
222 /* called from 'sort' without swap function, let's pick the default */
223 if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
224 swap_func = NULL;
225
226 if (!swap_func) {
227 if (is_aligned(base, size, 8))
228 swap_func = SWAP_WORDS_64;
229 else if (is_aligned(base, size, 4))
230 swap_func = SWAP_WORDS_32;
231 else
232 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 if (a) /* Building heap: sift down --a */
246 a -= size;
247 else if (n -= size) /* Sorting: Extract root to --n */
248 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 for (b = a; c = 2*b + size, (d = c + size) < n;)
265 b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d;
266 if (d == n) /* Special case last leaf with no sibling */
267 b = c;
268
269 /* Now backtrack from "b" to the correct location for "a" */
270 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
271 b = parent(b, lsbit, size);
272 c = b; /* Where "a" belongs */
273 while (b != a) { /* Shift it into place */
274 b = parent(b, lsbit, size);
275 do_swap(base + b, base + c, size, swap_func, priv);
276 }
277 }
278}
279EXPORT_SYMBOL(sort_r);
280
281void sort(void *base, size_t num, size_t size,
282 cmp_func_t cmp_func,
283 swap_func_t swap_func)
284{
285 struct wrapper w = {
286 .cmp = cmp_func,
287 .swap = swap_func,
288 };
289
290 return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
291}
292EXPORT_SYMBOL(sort);
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
33static 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 */
58static 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 */
83static 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 */
111static 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
130struct 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 */
139static 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
158static 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
184static 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 */
210void 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
219 if (!a) /* num < 2 || size == 0 */
220 return;
221
222 /* called from 'sort' without swap function, let's pick the default */
223 if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
224 swap_func = NULL;
225
226 if (!swap_func) {
227 if (is_aligned(base, size, 8))
228 swap_func = SWAP_WORDS_64;
229 else if (is_aligned(base, size, 4))
230 swap_func = SWAP_WORDS_32;
231 else
232 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 if (a) /* Building heap: sift down --a */
246 a -= size;
247 else if (n -= size) /* Sorting: Extract root to --n */
248 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 for (b = a; c = 2*b + size, (d = c + size) < n;)
265 b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d;
266 if (d == n) /* Special case last leaf with no sibling */
267 b = c;
268
269 /* Now backtrack from "b" to the correct location for "a" */
270 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)
271 b = parent(b, lsbit, size);
272 c = b; /* Where "a" belongs */
273 while (b != a) { /* Shift it into place */
274 b = parent(b, lsbit, size);
275 do_swap(base + b, base + c, size, swap_func, priv);
276 }
277 }
278}
279EXPORT_SYMBOL(sort_r);
280
281void sort(void *base, size_t num, size_t size,
282 cmp_func_t cmp_func,
283 swap_func_t swap_func)
284{
285 struct wrapper w = {
286 .cmp = cmp_func,
287 .swap = swap_func,
288 };
289
290 return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
291}
292EXPORT_SYMBOL(sort);