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272 lines
8.4 KiB
272 lines
8.4 KiB
// SPDX-License-Identifier: GPL-2.0 |
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/* |
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* A fast, small, non-recursive O(n log n) sort for the Linux kernel |
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* |
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* This performs n*log2(n) + 0.37*n + o(n) comparisons on average, |
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* and 1.5*n*log2(n) + O(n) in the (very contrived) worst case. |
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* |
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* Glibc qsort() manages n*log2(n) - 1.26*n for random inputs (1.63*n |
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* better) at the expense of stack usage and much larger code to avoid |
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* quicksort's O(n^2) worst case. |
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*/ |
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#define pr_fmt(fmt) KBUILD_MODNAME ": " fmt |
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#include <linux/types.h> |
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#include <linux/export.h> |
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#include <linux/sort.h> |
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/** |
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* is_aligned - is this pointer & size okay for word-wide copying? |
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* @base: pointer to data |
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* @size: size of each element |
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* @align: required alignment (typically 4 or 8) |
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* |
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* Returns true if elements can be copied using word loads and stores. |
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* The size must be a multiple of the alignment, and the base address must |
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* be if we do not have CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS. |
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* |
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* For some reason, gcc doesn't know to optimize "if (a & mask || b & mask)" |
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* to "if ((a | b) & mask)", so we do that by hand. |
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*/ |
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__attribute_const__ __always_inline |
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static bool is_aligned(const void *base, size_t size, unsigned char align) |
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{ |
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unsigned char lsbits = (unsigned char)size; |
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(void)base; |
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#ifndef CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS |
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lsbits |= (unsigned char)(uintptr_t)base; |
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#endif |
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return (lsbits & (align - 1)) == 0; |
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} |
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/** |
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* swap_words_32 - swap two elements in 32-bit chunks |
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* @a: pointer to the first element to swap |
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* @b: pointer to the second element to swap |
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* @n: element size (must be a multiple of 4) |
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* |
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* Exchange the two objects in memory. This exploits base+index addressing, |
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* which basically all CPUs have, to minimize loop overhead computations. |
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* |
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* For some reason, on x86 gcc 7.3.0 adds a redundant test of n at the |
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* bottom of the loop, even though the zero flag is still valid from the |
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* subtract (since the intervening mov instructions don't alter the flags). |
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* Gcc 8.1.0 doesn't have that problem. |
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*/ |
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static void swap_words_32(void *a, void *b, size_t n) |
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{ |
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do { |
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u32 t = *(u32 *)(a + (n -= 4)); |
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*(u32 *)(a + n) = *(u32 *)(b + n); |
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*(u32 *)(b + n) = t; |
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} while (n); |
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} |
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/** |
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* swap_words_64 - swap two elements in 64-bit chunks |
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* @a: pointer to the first element to swap |
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* @b: pointer to the second element to swap |
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* @n: element size (must be a multiple of 8) |
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* |
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* Exchange the two objects in memory. This exploits base+index |
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* addressing, which basically all CPUs have, to minimize loop overhead |
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* computations. |
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* |
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* We'd like to use 64-bit loads if possible. If they're not, emulating |
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* one requires base+index+4 addressing which x86 has but most other |
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* processors do not. If CONFIG_64BIT, we definitely have 64-bit loads, |
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* but it's possible to have 64-bit loads without 64-bit pointers (e.g. |
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* x32 ABI). Are there any cases the kernel needs to worry about? |
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*/ |
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static void swap_words_64(void *a, void *b, size_t n) |
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{ |
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do { |
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#ifdef CONFIG_64BIT |
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u64 t = *(u64 *)(a + (n -= 8)); |
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*(u64 *)(a + n) = *(u64 *)(b + n); |
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*(u64 *)(b + n) = t; |
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#else |
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/* Use two 32-bit transfers to avoid base+index+4 addressing */ |
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u32 t = *(u32 *)(a + (n -= 4)); |
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*(u32 *)(a + n) = *(u32 *)(b + n); |
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*(u32 *)(b + n) = t; |
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t = *(u32 *)(a + (n -= 4)); |
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*(u32 *)(a + n) = *(u32 *)(b + n); |
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*(u32 *)(b + n) = t; |
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#endif |
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} while (n); |
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} |
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/** |
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* swap_bytes - swap two elements a byte at a time |
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* @a: pointer to the first element to swap |
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* @b: pointer to the second element to swap |
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* @n: element size |
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* |
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* This is the fallback if alignment doesn't allow using larger chunks. |
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*/ |
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static void swap_bytes(void *a, void *b, size_t n) |
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{ |
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do { |
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char t = ((char *)a)[--n]; |
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((char *)a)[n] = ((char *)b)[n]; |
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((char *)b)[n] = t; |
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} while (n); |
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} |
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/* |
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* The values are arbitrary as long as they can't be confused with |
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* a pointer, but small integers make for the smallest compare |
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* instructions. |
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*/ |
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#define SWAP_WORDS_64 (swap_func_t)0 |
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#define SWAP_WORDS_32 (swap_func_t)1 |
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#define SWAP_BYTES (swap_func_t)2 |
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/* |
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* The function pointer is last to make tail calls most efficient if the |
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* compiler decides not to inline this function. |
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*/ |
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static void do_swap(void *a, void *b, size_t size, swap_func_t swap_func) |
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{ |
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if (swap_func == SWAP_WORDS_64) |
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swap_words_64(a, b, size); |
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else if (swap_func == SWAP_WORDS_32) |
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swap_words_32(a, b, size); |
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else if (swap_func == SWAP_BYTES) |
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swap_bytes(a, b, size); |
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else |
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swap_func(a, b, (int)size); |
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} |
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#define _CMP_WRAPPER ((cmp_r_func_t)0L) |
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static int do_cmp(const void *a, const void *b, cmp_r_func_t cmp, const void *priv) |
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{ |
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if (cmp == _CMP_WRAPPER) |
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return ((cmp_func_t)(priv))(a, b); |
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return cmp(a, b, priv); |
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} |
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/** |
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* parent - given the offset of the child, find the offset of the parent. |
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* @i: the offset of the heap element whose parent is sought. Non-zero. |
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* @lsbit: a precomputed 1-bit mask, equal to "size & -size" |
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* @size: size of each element |
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* |
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* In terms of array indexes, the parent of element j = @i/@size is simply |
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* (j-1)/2. But when working in byte offsets, we can't use implicit |
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* truncation of integer divides. |
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* |
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* Fortunately, we only need one bit of the quotient, not the full divide. |
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* @size has a least significant bit. That bit will be clear if @i is |
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* an even multiple of @size, and set if it's an odd multiple. |
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* |
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* Logically, we're doing "if (i & lsbit) i -= size;", but since the |
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* branch is unpredictable, it's done with a bit of clever branch-free |
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* code instead. |
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*/ |
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__attribute_const__ __always_inline |
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static size_t parent(size_t i, unsigned int lsbit, size_t size) |
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{ |
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i -= size; |
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i -= size & -(i & lsbit); |
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return i / 2; |
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} |
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/** |
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* sort_r - sort an array of elements |
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* @base: pointer to data to sort |
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* @num: number of elements |
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* @size: size of each element |
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* @cmp_func: pointer to comparison function |
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* @swap_func: pointer to swap function or NULL |
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* @priv: third argument passed to comparison function |
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* |
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* This function does a heapsort on the given array. You may provide |
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* a swap_func function if you need to do something more than a memory |
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* copy (e.g. fix up pointers or auxiliary data), but the built-in swap |
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* avoids a slow retpoline and so is significantly faster. |
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* |
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* Sorting time is O(n log n) both on average and worst-case. While |
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* quicksort is slightly faster on average, it suffers from exploitable |
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* O(n*n) worst-case behavior and extra memory requirements that make |
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* it less suitable for kernel use. |
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*/ |
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void sort_r(void *base, size_t num, size_t size, |
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cmp_r_func_t cmp_func, |
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swap_func_t swap_func, |
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const void *priv) |
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{ |
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/* pre-scale counters for performance */ |
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size_t n = num * size, a = (num/2) * size; |
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const unsigned int lsbit = size & -size; /* Used to find parent */ |
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if (!a) /* num < 2 || size == 0 */ |
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return; |
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if (!swap_func) { |
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if (is_aligned(base, size, 8)) |
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swap_func = SWAP_WORDS_64; |
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else if (is_aligned(base, size, 4)) |
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swap_func = SWAP_WORDS_32; |
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else |
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swap_func = SWAP_BYTES; |
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} |
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/* |
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* Loop invariants: |
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* 1. elements [a,n) satisfy the heap property (compare greater than |
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* all of their children), |
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* 2. elements [n,num*size) are sorted, and |
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* 3. a <= b <= c <= d <= n (whenever they are valid). |
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*/ |
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for (;;) { |
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size_t b, c, d; |
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if (a) /* Building heap: sift down --a */ |
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a -= size; |
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else if (n -= size) /* Sorting: Extract root to --n */ |
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do_swap(base, base + n, size, swap_func); |
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else /* Sort complete */ |
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break; |
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/* |
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* Sift element at "a" down into heap. This is the |
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* "bottom-up" variant, which significantly reduces |
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* calls to cmp_func(): we find the sift-down path all |
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* the way to the leaves (one compare per level), then |
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* backtrack to find where to insert the target element. |
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* |
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* Because elements tend to sift down close to the leaves, |
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* this uses fewer compares than doing two per level |
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* on the way down. (A bit more than half as many on |
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* average, 3/4 worst-case.) |
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*/ |
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for (b = a; c = 2*b + size, (d = c + size) < n;) |
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b = do_cmp(base + c, base + d, cmp_func, priv) >= 0 ? c : d; |
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if (d == n) /* Special case last leaf with no sibling */ |
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b = c; |
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/* Now backtrack from "b" to the correct location for "a" */ |
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while (b != a && do_cmp(base + a, base + b, cmp_func, priv) >= 0) |
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b = parent(b, lsbit, size); |
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c = b; /* Where "a" belongs */ |
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while (b != a) { /* Shift it into place */ |
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b = parent(b, lsbit, size); |
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do_swap(base + b, base + c, size, swap_func); |
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} |
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} |
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} |
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EXPORT_SYMBOL(sort_r); |
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void sort(void *base, size_t num, size_t size, |
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cmp_func_t cmp_func, |
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swap_func_t swap_func) |
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{ |
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return sort_r(base, num, size, _CMP_WRAPPER, swap_func, cmp_func); |
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} |
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EXPORT_SYMBOL(sort);
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