// 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 <linux/types.h> #include <linux/export.h> #include <linux/sort.h> /** * 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 stil 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); } typedef void (*swap_func_t)(void *a, void *b, int size); /* * 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); } /** * 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 - 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 * * 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(void *base, size_t num, size_t size, int (*cmp_func)(const void *, const void *), void (*swap_func)(void *, void *, int size)) { /* 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 = cmp_func(base + c, base + d) >= 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 && cmp_func(base + a, base + b) >= 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