1 // SPDX-License-Identifier: GPL-2.0
3 * A fast, small, non-recursive O(n log n) sort for the Linux kernel
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.
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.
13 #define pr_fmt(fmt) KBUILD_MODNAME ": " fmt
15 #include <linux/types.h>
16 #include <linux/export.h>
17 #include <linux/sort.h>
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)
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.
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.
32 __attribute_const__ __always_inline
33 static bool is_aligned(const void *base, size_t size, unsigned char align)
35 unsigned char lsbits = (unsigned char)size;
38 #ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS
39 lsbits |= (unsigned char)(uintptr_t)base;
41 return (lsbits & (align - 1)) == 0;
45 * swap_words_32 - swap two elements in 32-bit chunks
46 * @a, @b: pointers to the elements
47 * @size: element size (must be a multiple of 4)
49 * Exchange the two objects in memory. This exploits base+index addressing,
50 * which basically all CPUs have, to minimize loop overhead computations.
52 * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the
53 * bottom of the loop, even though the zero flag is stil valid from the
54 * subtract (since the intervening mov instructions don't alter the flags).
55 * Gcc 8.1.0 doesn't have that problem.
57 static void swap_words_32(void *a, void *b, int size)
59 size_t n = (unsigned int)size;
62 u32 t = *(u32 *)(a + (n -= 4));
63 *(u32 *)(a + n) = *(u32 *)(b + n);
69 * swap_words_64 - swap two elements in 64-bit chunks
70 * @a, @b: pointers to the elements
71 * @size: element size (must be a multiple of 8)
73 * Exchange the two objects in memory. This exploits base+index
74 * addressing, which basically all CPUs have, to minimize loop overhead
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?
83 static void swap_words_64(void *a, void *b, int size)
85 size_t n = (unsigned int)size;
89 u64 t = *(u64 *)(a + (n -= 8));
90 *(u64 *)(a + n) = *(u64 *)(b + n);
93 /* Use two 32-bit transfers to avoid base+index+4 addressing */
94 u32 t = *(u32 *)(a + (n -= 4));
95 *(u32 *)(a + n) = *(u32 *)(b + n);
98 t = *(u32 *)(a + (n -= 4));
99 *(u32 *)(a + n) = *(u32 *)(b + n);
106 * swap_bytes - swap two elements a byte at a time
107 * @a, @b: pointers to the elements
108 * @size: element size
110 * This is the fallback if alignment doesn't allow using larger chunks.
112 static void swap_bytes(void *a, void *b, int size)
114 size_t n = (unsigned int)size;
117 char t = ((char *)a)[--n];
118 ((char *)a)[n] = ((char *)b)[n];
124 * parent - given the offset of the child, find the offset of the parent.
125 * @i: the offset of the heap element whose parent is sought. Non-zero.
126 * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
127 * @size: size of each element
129 * In terms of array indexes, the parent of element j = @i/@size is simply
130 * (j-1)/2. But when working in byte offsets, we can't use implicit
131 * truncation of integer divides.
133 * Fortunately, we only need one bit of the quotient, not the full divide.
134 * @size has a least significant bit. That bit will be clear if @i is
135 * an even multiple of @size, and set if it's an odd multiple.
137 * Logically, we're doing "if (i & lsbit) i -= size;", but since the
138 * branch is unpredictable, it's done with a bit of clever branch-free
141 __attribute_const__ __always_inline
142 static size_t parent(size_t i, unsigned int lsbit, size_t size)
145 i -= size & -(i & lsbit);
150 * sort - sort an array of elements
151 * @base: pointer to data to sort
152 * @num: number of elements
153 * @size: size of each element
154 * @cmp_func: pointer to comparison function
155 * @swap_func: pointer to swap function or NULL
157 * This function does a heapsort on the given array. You may provide
158 * a swap_func function if you need to do something more than a memory
159 * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
160 * isn't usually a bottleneck.
162 * Sorting time is O(n log n) both on average and worst-case. While
163 * quicksort is slightly faster on average, it suffers from exploitable
164 * O(n*n) worst-case behavior and extra memory requirements that make
165 * it less suitable for kernel use.
167 void sort(void *base, size_t num, size_t size,
168 int (*cmp_func)(const void *, const void *),
169 void (*swap_func)(void *, void *, int size))
171 /* pre-scale counters for performance */
172 size_t n = num * size, a = (num/2) * size;
173 const unsigned int lsbit = size & -size; /* Used to find parent */
175 if (!a) /* num < 2 || size == 0 */
179 if (is_aligned(base, size, 8))
180 swap_func = swap_words_64;
181 else if (is_aligned(base, size, 4))
182 swap_func = swap_words_32;
184 swap_func = swap_bytes;
189 * 1. elements [a,n) satisfy the heap property (compare greater than
190 * all of their children),
191 * 2. elements [n,num*size) are sorted, and
192 * 3. a <= b <= c <= d <= n (whenever they are valid).
197 if (a) /* Building heap: sift down --a */
199 else if (n -= size) /* Sorting: Extract root to --n */
200 swap_func(base, base + n, size);
201 else /* Sort complete */
205 * Sift element at "a" down into heap. This is the
206 * "bottom-up" variant, which significantly reduces
207 * calls to cmp_func(): we find the sift-down path all
208 * the way to the leaves (one compare per level), then
209 * backtrack to find where to insert the target element.
211 * Because elements tend to sift down close to the leaves,
212 * this uses fewer compares than doing two per level
213 * on the way down. (A bit more than half as many on
214 * average, 3/4 worst-case.)
216 for (b = a; c = 2*b + size, (d = c + size) < n;)
217 b = cmp_func(base + c, base + d) >= 0 ? c : d;
218 if (d == n) /* Special case last leaf with no sibling */
221 /* Now backtrack from "b" to the correct location for "a" */
222 while (b != a && cmp_func(base + a, base + b) >= 0)
223 b = parent(b, lsbit, size);
224 c = b; /* Where "a" belongs */
225 while (b != a) { /* Shift it into place */
226 b = parent(b, lsbit, size);
227 swap_func(base + b, base + c, size);