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## Elixir Cross Referencer

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