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 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 */ 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 */ 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 */ 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_func_t)0 126 #define SWAP_WORDS_32 (swap_func_t)1 127 #define SWAP_BYTES (swap_func_t)2 128 129 /* 130 * The function pointer is last to make tail calls most efficient if the 131 * compiler decides not to inline this function. 132 */ 133 static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func) 134 { 135 if (swap_func == SWAP_WORDS_64) 136 swap_words_64(a, b, size); 137 else if (swap_func == SWAP_WORDS_32) 138 swap_words_32(a, b, size); 139 else if (swap_func == SWAP_BYTES) 140 swap_bytes(a, b, size); 141 else 142 swap_func(a, b, (int)size); 143 } 144 145 #define _CMP_WRAPPER ((cmp_r_func_t)0L) 146 147 static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv) 148 { 149 if (cmp == _CMP_WRAPPER) 150 return ((cmp_func_t)(priv))(a, b); 151 return cmp(a, b, priv); 152 } 153 154 /** 155 * parent - given the offset of the child, find the offset of the parent. 156 * @i: the offset of the heap element whose parent is sought. Non-zero. 157 * @lsbit: a precomputed 1-bit mask, equal to "size & -size" 158 * @size: size of each element 159 * 160 * In terms of array indexes, the parent of element j = @i/@size is simply 161 * (j-1)/2. But when working in byte offsets, we can't use implicit 162 * truncation of integer divides. 163 * 164 * Fortunately, we only need one bit of the quotient, not the full divide. 165 * @size has a least significant bit. That bit will be clear if @i is 166 * an even multiple of @size, and set if it's an odd multiple. 167 * 168 * Logically, we're doing "if (i & lsbit) i -= size;", but since the 169 * branch is unpredictable, it's done with a bit of clever branch-free 170 * code instead. 171 */ 172 __attribute_const__ __always_inline 173 static size_t parent(size_t i, unsigned int lsbit, size_t size) 174 { 175 i -= size; 176 i -= size & -(i & lsbit); 177 return i / 2; 178 } 179 180 /** 181 * sort_r - sort an array of elements 182 * @base: pointer to data to sort 183 * @num: number of elements 184 * @size: size of each element 185 * @cmp_func: pointer to comparison function 186 * @swap_func: pointer to swap function or NULL 187 * @priv: third argument passed to comparison function 188 * 189 * This function does a heapsort on the given array. You may provide 190 * a swap_func function if you need to do something more than a memory 191 * copy (e.g. fix up pointers or auxiliary data), but the built-in swap 192 * avoids a slow retpoline and so is significantly faster. 193 * 194 * Sorting time is O(n log n) both on average and worst-case. While 195 * quicksort is slightly faster on average, it suffers from exploitable 196 * O(n*n) worst-case behavior and extra memory requirements that make 197 * it less suitable for kernel use. 198 */ 199 void sort_r(void *base, size_t num, size_t size, 200 cmp_r_func_t cmp_func, 201 swap_func_t swap_func, 202 const void *priv) 203 { 204 /* pre-scale counters for performance */ 205 size_t n = num * size, a = (num/2) * size; 206 const unsigned int lsbit = size & -size; /* Used to find parent */ 207 208 if (!a) /* num < 2 || size == 0 */ 209 return; 210 211 if (!swap_func) { 212 if (is_aligned(base, size, 8)) 213 swap_func = SWAP_WORDS_64; 214 else if (is_aligned(base, size, 4)) 215 swap_func = SWAP_WORDS_32; 216 else 217 swap_func = SWAP_BYTES; 218 } 219 220 /* 221 * Loop invariants: 222 * 1. elements [a,n) satisfy the heap property (compare greater than 223 * all of their children), 224 * 2. elements [n,num*size) are sorted, and 225 * 3. a <= b <= c <= d <= n (whenever they are valid). 226 */ 227 for (;;) { 228 size_t b, c, d; 229 230 if (a) /* Building heap: sift down --a */ 231 a -= size; 232 else if (n -= size) /* Sorting: Extract root to --n */ 233 do_swap(base, base + n, size, swap_func); 234 else /* Sort complete */ 235 break; 236 237 /* 238 * Sift element at "a" down into heap. This is the 239 * "bottom-up" variant, which significantly reduces 240 * calls to cmp_func(): we find the sift-down path all 241 * the way to the leaves (one compare per level), then 242 * backtrack to find where to insert the target element. 243 * 244 * Because elements tend to sift down close to the leaves, 245 * this uses fewer compares than doing two per level 246 * on the way down. (A bit more than half as many on 247 * average, 3/4 worst-case.) 248 */ 249 for (b = a; c = 2*b + size, (d = c + size) < n;) 250 b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d; 251 if (d == n) /* Special case last leaf with no sibling */ 252 b = c; 253 254 /* Now backtrack from "b" to the correct location for "a" */ 255 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0) 256 b = parent(b, lsbit, size); 257 c = b; /* Where "a" belongs */ 258 while (b != a) { /* Shift it into place */ 259 b = parent(b, lsbit, size); 260 do_swap(base + b, base + c, size, swap_func); 261 } 262 } 263 } 264 EXPORT_SYMBOL(sort_r); 265 266 void sort(void *base, size_t num, size_t size, 267 cmp_func_t cmp_func, 268 swap_func_t swap_func) 269 { 270 return sort_r(base, num, size, _CMP_WRAPPER, swap_func, cmp_func); 271 } 272 EXPORT_SYMBOL(sort); 273