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, @b: pointers to the elements 47 * @size: element size (must be a multiple of 4) 48 * 49 * Exchange the two objects in memory. This exploits base+index addressing, 50 * which basically all CPUs have, to minimize loop overhead computations. 51 * 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. 56 */ 57 static void swap_words_32(void *a, void *b, size_t n) 58 { 59 do { 60 u32 t = *(u32 *)(a + (n -= 4)); 61 *(u32 *)(a + n) = *(u32 *)(b + n); 62 *(u32 *)(b + n) = t; 63 } while (n); 64 } 65 66 /** 67 * swap_words_64 - swap two elements in 64-bit chunks 68 * @a, @b: pointers to the elements 69 * @size: element size (must be a multiple of 8) 70 * 71 * Exchange the two objects in memory. This exploits base+index 72 * addressing, which basically all CPUs have, to minimize loop overhead 73 * computations. 74 * 75 * We'd like to use 64-bit loads if possible. If they're not, emulating 76 * one requires base+index+4 addressing which x86 has but most other 77 * processors do not. If CONFIG_64BIT, we definitely have 64-bit loads, 78 * but it's possible to have 64-bit loads without 64-bit pointers (e.g. 79 * x32 ABI). Are there any cases the kernel needs to worry about? 80 */ 81 static void swap_words_64(void *a, void *b, size_t n) 82 { 83 do { 84 #ifdef CONFIG_64BIT 85 u64 t = *(u64 *)(a + (n -= 8)); 86 *(u64 *)(a + n) = *(u64 *)(b + n); 87 *(u64 *)(b + n) = t; 88 #else 89 /* Use two 32-bit transfers to avoid base+index+4 addressing */ 90 u32 t = *(u32 *)(a + (n -= 4)); 91 *(u32 *)(a + n) = *(u32 *)(b + n); 92 *(u32 *)(b + n) = t; 93 94 t = *(u32 *)(a + (n -= 4)); 95 *(u32 *)(a + n) = *(u32 *)(b + n); 96 *(u32 *)(b + n) = t; 97 #endif 98 } while (n); 99 } 100 101 /** 102 * swap_bytes - swap two elements a byte at a time 103 * @a, @b: pointers to the elements 104 * @size: element size 105 * 106 * This is the fallback if alignment doesn't allow using larger chunks. 107 */ 108 static void swap_bytes(void *a, void *b, size_t n) 109 { 110 do { 111 char t = ((char *)a)[--n]; 112 ((char *)a)[n] = ((char *)b)[n]; 113 ((char *)b)[n] = t; 114 } while (n); 115 } 116 117 typedef void (*swap_func_t)(void *a, void *b, int size); 118 119 /* 120 * The values are arbitrary as long as they can't be confused with 121 * a pointer, but small integers make for the smallest compare 122 * instructions. 123 */ 124 #define SWAP_WORDS_64 (swap_func_t)0 125 #define SWAP_WORDS_32 (swap_func_t)1 126 #define SWAP_BYTES (swap_func_t)2 127 128 /* 129 * The function pointer is last to make tail calls most efficient if the 130 * compiler decides not to inline this function. 131 */ 132 static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func) 133 { 134 if (swap_func == SWAP_WORDS_64) 135 swap_words_64(a, b, size); 136 else if (swap_func == SWAP_WORDS_32) 137 swap_words_32(a, b, size); 138 else if (swap_func == SWAP_BYTES) 139 swap_bytes(a, b, size); 140 else 141 swap_func(a, b, (int)size); 142 } 143 144 /** 145 * parent - given the offset of the child, find the offset of the parent. 146 * @i: the offset of the heap element whose parent is sought. Non-zero. 147 * @lsbit: a precomputed 1-bit mask, equal to "size & -size" 148 * @size: size of each element 149 * 150 * In terms of array indexes, the parent of element j = @i/@size is simply 151 * (j-1)/2. But when working in byte offsets, we can't use implicit 152 * truncation of integer divides. 153 * 154 * Fortunately, we only need one bit of the quotient, not the full divide. 155 * @size has a least significant bit. That bit will be clear if @i is 156 * an even multiple of @size, and set if it's an odd multiple. 157 * 158 * Logically, we're doing "if (i & lsbit) i -= size;", but since the 159 * branch is unpredictable, it's done with a bit of clever branch-free 160 * code instead. 161 */ 162 __attribute_const__ __always_inline 163 static size_t parent(size_t i, unsigned int lsbit, size_t size) 164 { 165 i -= size; 166 i -= size & -(i & lsbit); 167 return i / 2; 168 } 169 170 /** 171 * sort - sort an array of elements 172 * @base: pointer to data to sort 173 * @num: number of elements 174 * @size: size of each element 175 * @cmp_func: pointer to comparison function 176 * @swap_func: pointer to swap function or NULL 177 * 178 * This function does a heapsort on the given array. You may provide 179 * a swap_func function if you need to do something more than a memory 180 * copy (e.g. fix up pointers or auxiliary data), but the built-in swap 181 * avoids a slow retpoline and so is significantly faster. 182 * 183 * Sorting time is O(n log n) both on average and worst-case. While 184 * quicksort is slightly faster on average, it suffers from exploitable 185 * O(n*n) worst-case behavior and extra memory requirements that make 186 * it less suitable for kernel use. 187 */ 188 void sort(void *base, size_t num, size_t size, 189 int (*cmp_func)(const void *, const void *), 190 void (*swap_func)(void *, void *, int size)) 191 { 192 /* pre-scale counters for performance */ 193 size_t n = num * size, a = (num/2) * size; 194 const unsigned int lsbit = size & -size; /* Used to find parent */ 195 196 if (!a) /* num < 2 || size == 0 */ 197 return; 198 199 if (!swap_func) { 200 if (is_aligned(base, size, 8)) 201 swap_func = SWAP_WORDS_64; 202 else if (is_aligned(base, size, 4)) 203 swap_func = SWAP_WORDS_32; 204 else 205 swap_func = SWAP_BYTES; 206 } 207 208 /* 209 * Loop invariants: 210 * 1. elements [a,n) satisfy the heap property (compare greater than 211 * all of their children), 212 * 2. elements [n,num*size) are sorted, and 213 * 3. a <= b <= c <= d <= n (whenever they are valid). 214 */ 215 for (;;) { 216 size_t b, c, d; 217 218 if (a) /* Building heap: sift down --a */ 219 a -= size; 220 else if (n -= size) /* Sorting: Extract root to --n */ 221 do_swap(base, base + n, size, swap_func); 222 else /* Sort complete */ 223 break; 224 225 /* 226 * Sift element at "a" down into heap. This is the 227 * "bottom-up" variant, which significantly reduces 228 * calls to cmp_func(): we find the sift-down path all 229 * the way to the leaves (one compare per level), then 230 * backtrack to find where to insert the target element. 231 * 232 * Because elements tend to sift down close to the leaves, 233 * this uses fewer compares than doing two per level 234 * on the way down. (A bit more than half as many on 235 * average, 3/4 worst-case.) 236 */ 237 for (b = a; c = 2*b + size, (d = c + size) < n;) 238 b = cmp_func(base + c, base + d) >= 0 ? c : d; 239 if (d == n) /* Special case last leaf with no sibling */ 240 b = c; 241 242 /* Now backtrack from "b" to the correct location for "a" */ 243 while (b != a && cmp_func(base + a, base + b) >= 0) 244 b = parent(b, lsbit, size); 245 c = b; /* Where "a" belongs */ 246 while (b != a) { /* Shift it into place */ 247 b = parent(b, lsbit, size); 248 do_swap(base + b, base + c, size, swap_func); 249 } 250 } 251 } 252 EXPORT_SYMBOL(sort); 253