.. | .. |
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1 | 1 | // SPDX-License-Identifier: GPL-2.0 |
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2 | 2 | /* |
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3 | | - * A fast, small, non-recursive O(nlog n) sort for the Linux kernel |
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| 3 | + * A fast, small, non-recursive O(n log n) sort for the Linux kernel |
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4 | 4 | * |
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5 | | - * Jan 23 2005 Matt Mackall <mpm@selenic.com> |
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| 5 | + * This performs n*log2(n) + 0.37*n + o(n) comparisons on average, |
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| 6 | + * and 1.5*n*log2(n) + O(n) in the (very contrived) worst case. |
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| 7 | + * |
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| 8 | + * Glibc qsort() manages n*log2(n) - 1.26*n for random inputs (1.63*n |
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| 9 | + * better) at the expense of stack usage and much larger code to avoid |
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| 10 | + * quicksort's O(n^2) worst case. |
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6 | 11 | */ |
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7 | 12 | |
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8 | 13 | #define pr_fmt(fmt) KBUILD_MODNAME ": " fmt |
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.. | .. |
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11 | 16 | #include <linux/export.h> |
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12 | 17 | #include <linux/sort.h> |
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13 | 18 | |
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14 | | -static int alignment_ok(const void *base, int align) |
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| 19 | +/** |
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| 20 | + * is_aligned - is this pointer & size okay for word-wide copying? |
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| 21 | + * @base: pointer to data |
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| 22 | + * @size: size of each element |
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| 23 | + * @align: required alignment (typically 4 or 8) |
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| 24 | + * |
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| 25 | + * Returns true if elements can be copied using word loads and stores. |
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| 26 | + * The size must be a multiple of the alignment, and the base address must |
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| 27 | + * be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS. |
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| 28 | + * |
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| 29 | + * For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)" |
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| 30 | + * to "if ((a | b) & mask)", so we do that by hand. |
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| 31 | + */ |
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| 32 | +__attribute_const__ __always_inline |
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| 33 | +static bool is_aligned(const void *base, size_t size, unsigned char align) |
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15 | 34 | { |
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16 | | - return IS_ENABLED(CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS) || |
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17 | | - ((unsigned long)base & (align - 1)) == 0; |
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18 | | -} |
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| 35 | + unsigned char lsbits = (unsigned char)size; |
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19 | 36 | |
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20 | | -static void u32_swap(void *a, void *b, int size) |
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21 | | -{ |
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22 | | - u32 t = *(u32 *)a; |
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23 | | - *(u32 *)a = *(u32 *)b; |
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24 | | - *(u32 *)b = t; |
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25 | | -} |
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26 | | - |
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27 | | -static void u64_swap(void *a, void *b, int size) |
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28 | | -{ |
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29 | | - u64 t = *(u64 *)a; |
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30 | | - *(u64 *)a = *(u64 *)b; |
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31 | | - *(u64 *)b = t; |
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32 | | -} |
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33 | | - |
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34 | | -static void generic_swap(void *a, void *b, int size) |
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35 | | -{ |
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36 | | - char t; |
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37 | | - |
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38 | | - do { |
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39 | | - t = *(char *)a; |
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40 | | - *(char *)a++ = *(char *)b; |
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41 | | - *(char *)b++ = t; |
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42 | | - } while (--size > 0); |
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| 37 | + (void)base; |
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| 38 | +#ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS |
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| 39 | + lsbits |= (unsigned char)(uintptr_t)base; |
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| 40 | +#endif |
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| 41 | + return (lsbits & (align - 1)) == 0; |
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43 | 42 | } |
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44 | 43 | |
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45 | 44 | /** |
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46 | | - * sort - sort an array of elements |
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| 45 | + * swap_words_32 - swap two elements in 32-bit chunks |
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| 46 | + * @a: pointer to the first element to swap |
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| 47 | + * @b: pointer to the second element to swap |
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| 48 | + * @n: element size (must be a multiple of 4) |
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| 49 | + * |
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| 50 | + * Exchange the two objects in memory. This exploits base+index addressing, |
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| 51 | + * which basically all CPUs have, to minimize loop overhead computations. |
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| 52 | + * |
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| 53 | + * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the |
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| 54 | + * bottom of the loop, even though the zero flag is stil valid from the |
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| 55 | + * subtract (since the intervening mov instructions don't alter the flags). |
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| 56 | + * Gcc 8.1.0 doesn't have that problem. |
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| 57 | + */ |
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| 58 | +static void swap_words_32(void *a, void *b, size_t n) |
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| 59 | +{ |
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| 60 | + do { |
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| 61 | + u32 t = *(u32 *)(a + (n -= 4)); |
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| 62 | + *(u32 *)(a + n) = *(u32 *)(b + n); |
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| 63 | + *(u32 *)(b + n) = t; |
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| 64 | + } while (n); |
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| 65 | +} |
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| 66 | + |
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| 67 | +/** |
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| 68 | + * swap_words_64 - swap two elements in 64-bit chunks |
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| 69 | + * @a: pointer to the first element to swap |
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| 70 | + * @b: pointer to the second element to swap |
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| 71 | + * @n: element size (must be a multiple of 8) |
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| 72 | + * |
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| 73 | + * Exchange the two objects in memory. This exploits base+index |
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| 74 | + * addressing, which basically all CPUs have, to minimize loop overhead |
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| 75 | + * computations. |
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| 76 | + * |
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| 77 | + * We'd like to use 64-bit loads if possible. If they're not, emulating |
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| 78 | + * one requires base+index+4 addressing which x86 has but most other |
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| 79 | + * processors do not. If CONFIG_64BIT, we definitely have 64-bit loads, |
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| 80 | + * but it's possible to have 64-bit loads without 64-bit pointers (e.g. |
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| 81 | + * x32 ABI). Are there any cases the kernel needs to worry about? |
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| 82 | + */ |
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| 83 | +static void swap_words_64(void *a, void *b, size_t n) |
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| 84 | +{ |
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| 85 | + do { |
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| 86 | +#ifdef CONFIG_64BIT |
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| 87 | + u64 t = *(u64 *)(a + (n -= 8)); |
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| 88 | + *(u64 *)(a + n) = *(u64 *)(b + n); |
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| 89 | + *(u64 *)(b + n) = t; |
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| 90 | +#else |
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| 91 | + /* Use two 32-bit transfers to avoid base+index+4 addressing */ |
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| 92 | + u32 t = *(u32 *)(a + (n -= 4)); |
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| 93 | + *(u32 *)(a + n) = *(u32 *)(b + n); |
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| 94 | + *(u32 *)(b + n) = t; |
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| 95 | + |
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| 96 | + t = *(u32 *)(a + (n -= 4)); |
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| 97 | + *(u32 *)(a + n) = *(u32 *)(b + n); |
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| 98 | + *(u32 *)(b + n) = t; |
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| 99 | +#endif |
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| 100 | + } while (n); |
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| 101 | +} |
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| 102 | + |
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| 103 | +/** |
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| 104 | + * swap_bytes - swap two elements a byte at a time |
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| 105 | + * @a: pointer to the first element to swap |
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| 106 | + * @b: pointer to the second element to swap |
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| 107 | + * @n: element size |
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| 108 | + * |
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| 109 | + * This is the fallback if alignment doesn't allow using larger chunks. |
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| 110 | + */ |
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| 111 | +static void swap_bytes(void *a, void *b, size_t n) |
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| 112 | +{ |
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| 113 | + do { |
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| 114 | + char t = ((char *)a)[--n]; |
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| 115 | + ((char *)a)[n] = ((char *)b)[n]; |
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| 116 | + ((char *)b)[n] = t; |
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| 117 | + } while (n); |
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| 118 | +} |
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| 119 | + |
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| 120 | +/* |
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| 121 | + * The values are arbitrary as long as they can't be confused with |
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| 122 | + * a pointer, but small integers make for the smallest compare |
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| 123 | + * instructions. |
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| 124 | + */ |
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| 125 | +#define SWAP_WORDS_64 (swap_func_t)0 |
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| 126 | +#define SWAP_WORDS_32 (swap_func_t)1 |
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| 127 | +#define SWAP_BYTES (swap_func_t)2 |
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| 128 | + |
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| 129 | +/* |
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| 130 | + * The function pointer is last to make tail calls most efficient if the |
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| 131 | + * compiler decides not to inline this function. |
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| 132 | + */ |
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| 133 | +static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func) |
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| 134 | +{ |
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| 135 | + if (swap_func == SWAP_WORDS_64) |
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| 136 | + swap_words_64(a, b, size); |
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| 137 | + else if (swap_func == SWAP_WORDS_32) |
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| 138 | + swap_words_32(a, b, size); |
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| 139 | + else if (swap_func == SWAP_BYTES) |
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| 140 | + swap_bytes(a, b, size); |
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| 141 | + else |
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| 142 | + swap_func(a, b, (int)size); |
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| 143 | +} |
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| 144 | + |
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| 145 | +#define _CMP_WRAPPER ((cmp_r_func_t)0L) |
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| 146 | + |
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| 147 | +static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv) |
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| 148 | +{ |
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| 149 | + if (cmp == _CMP_WRAPPER) |
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| 150 | + return ((cmp_func_t)(priv))(a, b); |
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| 151 | + return cmp(a, b, priv); |
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| 152 | +} |
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| 153 | + |
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| 154 | +/** |
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| 155 | + * parent - given the offset of the child, find the offset of the parent. |
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| 156 | + * @i: the offset of the heap element whose parent is sought. Non-zero. |
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| 157 | + * @lsbit: a precomputed 1-bit mask, equal to "size & -size" |
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| 158 | + * @size: size of each element |
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| 159 | + * |
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| 160 | + * In terms of array indexes, the parent of element j = @i/@size is simply |
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| 161 | + * (j-1)/2. But when working in byte offsets, we can't use implicit |
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| 162 | + * truncation of integer divides. |
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| 163 | + * |
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| 164 | + * Fortunately, we only need one bit of the quotient, not the full divide. |
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| 165 | + * @size has a least significant bit. That bit will be clear if @i is |
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| 166 | + * an even multiple of @size, and set if it's an odd multiple. |
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| 167 | + * |
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| 168 | + * Logically, we're doing "if (i & lsbit) i -= size;", but since the |
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| 169 | + * branch is unpredictable, it's done with a bit of clever branch-free |
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| 170 | + * code instead. |
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| 171 | + */ |
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| 172 | +__attribute_const__ __always_inline |
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| 173 | +static size_t parent(size_t i, unsigned int lsbit, size_t size) |
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| 174 | +{ |
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| 175 | + i -= size; |
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| 176 | + i -= size & -(i & lsbit); |
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| 177 | + return i / 2; |
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| 178 | +} |
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| 179 | + |
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| 180 | +/** |
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| 181 | + * sort_r - sort an array of elements |
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47 | 182 | * @base: pointer to data to sort |
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48 | 183 | * @num: number of elements |
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49 | 184 | * @size: size of each element |
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50 | 185 | * @cmp_func: pointer to comparison function |
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51 | 186 | * @swap_func: pointer to swap function or NULL |
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| 187 | + * @priv: third argument passed to comparison function |
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52 | 188 | * |
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53 | | - * This function does a heapsort on the given array. You may provide a |
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54 | | - * swap_func function optimized to your element type. |
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| 189 | + * This function does a heapsort on the given array. You may provide |
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| 190 | + * a swap_func function if you need to do something more than a memory |
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| 191 | + * copy (e.g. fix up pointers or auxiliary data), but the built-in swap |
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| 192 | + * avoids a slow retpoline and so is significantly faster. |
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55 | 193 | * |
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56 | 194 | * Sorting time is O(n log n) both on average and worst-case. While |
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57 | | - * qsort is about 20% faster on average, it suffers from exploitable |
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| 195 | + * quicksort is slightly faster on average, it suffers from exploitable |
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58 | 196 | * O(n*n) worst-case behavior and extra memory requirements that make |
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59 | 197 | * it less suitable for kernel use. |
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60 | 198 | */ |
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61 | | - |
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62 | | -void sort(void *base, size_t num, size_t size, |
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63 | | - int (*cmp_func)(const void *, const void *), |
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64 | | - void (*swap_func)(void *, void *, int size)) |
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| 199 | +void sort_r(void *base, size_t num, size_t size, |
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| 200 | + cmp_r_func_t cmp_func, |
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| 201 | + swap_func_t swap_func, |
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| 202 | + const void *priv) |
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65 | 203 | { |
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66 | 204 | /* pre-scale counters for performance */ |
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67 | | - int i = (num/2 - 1) * size, n = num * size, c, r; |
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| 205 | + size_t n = num * size, a = (num/2) * size; |
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| 206 | + const unsigned int lsbit = size & -size; /* Used to find parent */ |
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| 207 | + |
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| 208 | + if (!a) /* num < 2 || size == 0 */ |
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| 209 | + return; |
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68 | 210 | |
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69 | 211 | if (!swap_func) { |
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70 | | - if (size == 4 && alignment_ok(base, 4)) |
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71 | | - swap_func = u32_swap; |
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72 | | - else if (size == 8 && alignment_ok(base, 8)) |
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73 | | - swap_func = u64_swap; |
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| 212 | + if (is_aligned(base, size, 8)) |
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| 213 | + swap_func = SWAP_WORDS_64; |
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| 214 | + else if (is_aligned(base, size, 4)) |
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| 215 | + swap_func = SWAP_WORDS_32; |
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74 | 216 | else |
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75 | | - swap_func = generic_swap; |
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| 217 | + swap_func = SWAP_BYTES; |
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76 | 218 | } |
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77 | 219 | |
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78 | | - /* heapify */ |
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79 | | - for ( ; i >= 0; i -= size) { |
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80 | | - for (r = i; r * 2 + size < n; r = c) { |
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81 | | - c = r * 2 + size; |
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82 | | - if (c < n - size && |
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83 | | - cmp_func(base + c, base + c + size) < 0) |
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84 | | - c += size; |
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85 | | - if (cmp_func(base + r, base + c) >= 0) |
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86 | | - break; |
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87 | | - swap_func(base + r, base + c, size); |
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88 | | - } |
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89 | | - } |
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| 220 | + /* |
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| 221 | + * Loop invariants: |
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| 222 | + * 1. elements [a,n) satisfy the heap property (compare greater than |
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| 223 | + * all of their children), |
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| 224 | + * 2. elements [n,num*size) are sorted, and |
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| 225 | + * 3. a <= b <= c <= d <= n (whenever they are valid). |
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| 226 | + */ |
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| 227 | + for (;;) { |
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| 228 | + size_t b, c, d; |
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90 | 229 | |
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91 | | - /* sort */ |
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92 | | - for (i = n - size; i > 0; i -= size) { |
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93 | | - swap_func(base, base + i, size); |
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94 | | - for (r = 0; r * 2 + size < i; r = c) { |
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95 | | - c = r * 2 + size; |
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96 | | - if (c < i - size && |
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97 | | - cmp_func(base + c, base + c + size) < 0) |
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98 | | - c += size; |
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99 | | - if (cmp_func(base + r, base + c) >= 0) |
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100 | | - break; |
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101 | | - swap_func(base + r, base + c, size); |
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| 230 | + if (a) /* Building heap: sift down --a */ |
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| 231 | + a -= size; |
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| 232 | + else if (n -= size) /* Sorting: Extract root to --n */ |
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| 233 | + do_swap(base, base + n, size, swap_func); |
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| 234 | + else /* Sort complete */ |
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| 235 | + break; |
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| 236 | + |
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| 237 | + /* |
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| 238 | + * Sift element at "a" down into heap. This is the |
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| 239 | + * "bottom-up" variant, which significantly reduces |
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| 240 | + * calls to cmp_func(): we find the sift-down path all |
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| 241 | + * the way to the leaves (one compare per level), then |
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| 242 | + * backtrack to find where to insert the target element. |
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| 243 | + * |
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| 244 | + * Because elements tend to sift down close to the leaves, |
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| 245 | + * this uses fewer compares than doing two per level |
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| 246 | + * on the way down. (A bit more than half as many on |
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| 247 | + * average, 3/4 worst-case.) |
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| 248 | + */ |
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| 249 | + for (b = a; c = 2*b + size, (d = c + size) < n;) |
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| 250 | + b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d; |
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| 251 | + if (d == n) /* Special case last leaf with no sibling */ |
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| 252 | + b = c; |
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| 253 | + |
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| 254 | + /* Now backtrack from "b" to the correct location for "a" */ |
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| 255 | + while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0) |
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| 256 | + b = parent(b, lsbit, size); |
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| 257 | + c = b; /* Where "a" belongs */ |
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| 258 | + while (b != a) { /* Shift it into place */ |
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| 259 | + b = parent(b, lsbit, size); |
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| 260 | + do_swap(base + b, base + c, size, swap_func); |
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102 | 261 | } |
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103 | 262 | } |
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104 | 263 | } |
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| 264 | +EXPORT_SYMBOL(sort_r); |
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105 | 265 | |
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| 266 | +void sort(void *base, size_t num, size_t size, |
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| 267 | + cmp_func_t cmp_func, |
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| 268 | + swap_func_t swap_func) |
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| 269 | +{ |
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| 270 | + return sort_r(base, num, size, _CMP_WRAPPER, swap_func, cmp_func); |
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| 271 | +} |
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106 | 272 | EXPORT_SYMBOL(sort); |
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