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1// SPDX-License-Identifier: GPL-2.02/*3 * A fast, small, non-recursive O(n log n) sort for the Linux kernel4 *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 * Quicksort manages n*log2(n) - 1.26*n for random inputs (1.63*n9 * better) at the expense of stack usage and much larger code to avoid10 * quicksort's O(n^2) worst case.11 */12 13#include <linux/types.h>14#include <linux/export.h>15#include <linux/sort.h>16 17/**18 * is_aligned - is this pointer & size okay for word-wide copying?19 * @base: pointer to data20 * @size: size of each element21 * @align: required alignment (typically 4 or 8)22 *23 * Returns true if elements can be copied using word loads and stores.24 * The size must be a multiple of the alignment, and the base address must25 * be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS.26 *27 * For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)"28 * to "if ((a | b) & mask)", so we do that by hand.29 */30__attribute_const__ __always_inline31static bool is_aligned(const void *base, size_t size, unsigned char align)32{33 unsigned char lsbits = (unsigned char)size;34 35 (void)base;36#ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS37 lsbits |= (unsigned char)(uintptr_t)base;38#endif39 return (lsbits & (align - 1)) == 0;40}41 42/**43 * swap_words_32 - swap two elements in 32-bit chunks44 * @a: pointer to the first element to swap45 * @b: pointer to the second element to swap46 * @n: element size (must be a multiple of 4)47 *48 * Exchange the two objects in memory. This exploits base+index addressing,49 * which basically all CPUs have, to minimize loop overhead computations.50 *51 * For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the52 * bottom of the loop, even though the zero flag is still valid from the53 * subtract (since the intervening mov instructions don't alter the flags).54 * Gcc 8.1.0 doesn't have that problem.55 */56static void swap_words_32(void *a, void *b, size_t n)57{58 do {59 u32 t = *(u32 *)(a + (n -= 4));60 *(u32 *)(a + n) = *(u32 *)(b + n);61 *(u32 *)(b + n) = t;62 } while (n);63}64 65/**66 * swap_words_64 - swap two elements in 64-bit chunks67 * @a: pointer to the first element to swap68 * @b: pointer to the second element to swap69 * @n: element size (must be a multiple of 8)70 *71 * Exchange the two objects in memory. This exploits base+index72 * addressing, which basically all CPUs have, to minimize loop overhead73 * computations.74 *75 * We'd like to use 64-bit loads if possible. If they're not, emulating76 * one requires base+index+4 addressing which x86 has but most other77 * 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 */81static void swap_words_64(void *a, void *b, size_t n)82{83 do {84#ifdef CONFIG_64BIT85 u64 t = *(u64 *)(a + (n -= 8));86 *(u64 *)(a + n) = *(u64 *)(b + n);87 *(u64 *)(b + n) = t;88#else89 /* 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#endif98 } while (n);99}100 101/**102 * swap_bytes - swap two elements a byte at a time103 * @a: pointer to the first element to swap104 * @b: pointer to the second element to swap105 * @n: element size106 *107 * This is the fallback if alignment doesn't allow using larger chunks.108 */109static void swap_bytes(void *a, void *b, size_t n)110{111 do {112 char t = ((char *)a)[--n];113 ((char *)a)[n] = ((char *)b)[n];114 ((char *)b)[n] = t;115 } while (n);116}117 118/*119 * The values are arbitrary as long as they can't be confused with120 * a pointer, but small integers make for the smallest compare121 * instructions.122 */123#define SWAP_WORDS_64 (swap_r_func_t)0124#define SWAP_WORDS_32 (swap_r_func_t)1125#define SWAP_BYTES (swap_r_func_t)2126#define SWAP_WRAPPER (swap_r_func_t)3127 128struct wrapper {129 cmp_func_t cmp;130 swap_func_t swap;131};132 133/*134 * The function pointer is last to make tail calls most efficient if the135 * compiler decides not to inline this function.136 */137static void do_swap(void *a, void *b, size_t size, swap_r_func_t swap_func, const void *priv)138{139 if (swap_func == SWAP_WRAPPER) {140 ((const struct wrapper *)priv)->swap(a, b, (int)size);141 return;142 }143 144 if (swap_func == SWAP_WORDS_64)145 swap_words_64(a, b, size);146 else if (swap_func == SWAP_WORDS_32)147 swap_words_32(a, b, size);148 else if (swap_func == SWAP_BYTES)149 swap_bytes(a, b, size);150 else151 swap_func(a, b, (int)size, priv);152}153 154#define _CMP_WRAPPER ((cmp_r_func_t)0L)155 156static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv)157{158 if (cmp == _CMP_WRAPPER)159 return ((const struct wrapper *)priv)->cmp(a, b);160 return cmp(a, b, priv);161}162 163/**164 * parent - given the offset of the child, find the offset of the parent.165 * @i: the offset of the heap element whose parent is sought. Non-zero.166 * @lsbit: a precomputed 1-bit mask, equal to "size & -size"167 * @size: size of each element168 *169 * In terms of array indexes, the parent of element j = @i/@size is simply170 * (j-1)/2. But when working in byte offsets, we can't use implicit171 * truncation of integer divides.172 *173 * Fortunately, we only need one bit of the quotient, not the full divide.174 * @size has a least significant bit. That bit will be clear if @i is175 * an even multiple of @size, and set if it's an odd multiple.176 *177 * Logically, we're doing "if (i & lsbit) i -= size;", but since the178 * branch is unpredictable, it's done with a bit of clever branch-free179 * code instead.180 */181__attribute_const__ __always_inline182static size_t parent(size_t i, unsigned int lsbit, size_t size)183{184 i -= size;185 i -= size & -(i & lsbit);186 return i / 2;187}188 189/**190 * sort_r - sort an array of elements191 * @base: pointer to data to sort192 * @num: number of elements193 * @size: size of each element194 * @cmp_func: pointer to comparison function195 * @swap_func: pointer to swap function or NULL196 * @priv: third argument passed to comparison function197 *198 * This function does a heapsort on the given array. You may provide199 * a swap_func function if you need to do something more than a memory200 * copy (e.g. fix up pointers or auxiliary data), but the built-in swap201 * avoids a slow retpoline and so is significantly faster.202 *203 * Sorting time is O(n log n) both on average and worst-case. While204 * quicksort is slightly faster on average, it suffers from exploitable205 * O(n*n) worst-case behavior and extra memory requirements that make206 * it less suitable for kernel use.207 */208void sort_r(void *base, size_t num, size_t size,209 cmp_r_func_t cmp_func,210 swap_r_func_t swap_func,211 const void *priv)212{213 /* pre-scale counters for performance */214 size_t n = num * size, a = (num/2) * size;215 const unsigned int lsbit = size & -size; /* Used to find parent */216 size_t shift = 0;217 218 if (!a) /* num < 2 || size == 0 */219 return;220 221 /* called from 'sort' without swap function, let's pick the default */222 if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)223 swap_func = NULL;224 225 if (!swap_func) {226 if (is_aligned(base, size, 8))227 swap_func = SWAP_WORDS_64;228 else if (is_aligned(base, size, 4))229 swap_func = SWAP_WORDS_32;230 else231 swap_func = SWAP_BYTES;232 }233 234 /*235 * Loop invariants:236 * 1. elements [a,n) satisfy the heap property (compare greater than237 * all of their children),238 * 2. elements [n,num*size) are sorted, and239 * 3. a <= b <= c <= d <= n (whenever they are valid).240 */241 for (;;) {242 size_t b, c, d;243 244 if (a) /* Building heap: sift down a */245 a -= size << shift;246 else if (n > 3 * size) { /* Sorting: Extract two largest elements */247 n -= size;248 do_swap(base, base + n, size, swap_func, priv);249 shift = do_cmp(base + size, base + 2 * size, cmp_func, priv) <= 0;250 a = size << shift;251 n -= size;252 do_swap(base + a, base + n, size, swap_func, priv);253 } else { /* Sort complete */254 break;255 }256 257 /*258 * Sift element at "a" down into heap. This is the259 * "bottom-up" variant, which significantly reduces260 * calls to cmp_func(): we find the sift-down path all261 * the way to the leaves (one compare per level), then262 * backtrack to find where to insert the target element.263 *264 * Because elements tend to sift down close to the leaves,265 * this uses fewer compares than doing two per level266 * on the way down. (A bit more than half as many on267 * average, 3/4 worst-case.)268 */269 for (b = a; c = 2*b + size, (d = c + size) < n;)270 b = do_cmp(base + c, base + d, cmp_func, priv) > 0 ? c : d;271 if (d == n) /* Special case last leaf with no sibling */272 b = c;273 274 /* Now backtrack from "b" to the correct location for "a" */275 while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0)276 b = parent(b, lsbit, size);277 c = b; /* Where "a" belongs */278 while (b != a) { /* Shift it into place */279 b = parent(b, lsbit, size);280 do_swap(base + b, base + c, size, swap_func, priv);281 }282 }283 284 n -= size;285 do_swap(base, base + n, size, swap_func, priv);286 if (n == size * 2 && do_cmp(base, base + size, cmp_func, priv) > 0)287 do_swap(base, base + size, size, swap_func, priv);288}289EXPORT_SYMBOL(sort_r);290 291void sort(void *base, size_t num, size_t size,292 cmp_func_t cmp_func,293 swap_func_t swap_func)294{295 struct wrapper w = {296 .cmp = cmp_func,297 .swap = swap_func,298 };299 300 return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);301}302EXPORT_SYMBOL(sort);303