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Diffstat (limited to 'lib/sort.c')
| -rw-r--r-- | lib/sort.c | 292 |
1 files changed, 292 insertions, 0 deletions
diff --git a/lib/sort.c b/lib/sort.c new file mode 100644 index 0000000000..b399bf10d6 --- /dev/null +++ b/lib/sort.c @@ -0,0 +1,292 @@ +// 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 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_r_func_t)0 +#define SWAP_WORDS_32 (swap_r_func_t)1 +#define SWAP_BYTES (swap_r_func_t)2 +#define SWAP_WRAPPER (swap_r_func_t)3 + +struct wrapper { + cmp_func_t cmp; + swap_func_t swap; +}; + +/* + * 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_r_func_t swap_func, const void *priv) +{ + if (swap_func == SWAP_WRAPPER) { + ((const struct wrapper *)priv)->swap(a, b, (int)size); + return; + } + + 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, priv); +} + +#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 ((const struct wrapper *)priv)->cmp(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_r_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; + + /* called from 'sort' without swap function, let's pick the default */ + if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap) + swap_func = NULL; + + 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, priv); + 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, priv); + } + } +} +EXPORT_SYMBOL(sort_r); + +void sort(void *base, size_t num, size_t size, + cmp_func_t cmp_func, + swap_func_t swap_func) +{ + struct wrapper w = { + .cmp = cmp_func, + .swap = swap_func, + }; + + return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w); +} +EXPORT_SYMBOL(sort); |