293 lines
8.9 KiB
C
293 lines
8.9 KiB
C
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// 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_r_func_t)0
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#define SWAP_WORDS_32 (swap_r_func_t)1
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#define SWAP_BYTES (swap_r_func_t)2
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#define SWAP_WRAPPER (swap_r_func_t)3
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struct wrapper {
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cmp_func_t cmp;
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swap_func_t swap;
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};
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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_r_func_t swap_func, const void *priv)
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{
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if (swap_func == SWAP_WRAPPER) {
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((const struct wrapper *)priv)->swap(a, b, (int)size);
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return;
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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, priv);
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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 ((const struct wrapper *)priv)->cmp(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_r_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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/* called from 'sort' without swap function, let's pick the default */
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if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap)
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swap_func = NULL;
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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, priv);
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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, priv);
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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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struct wrapper w = {
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.cmp = cmp_func,
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.swap = swap_func,
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};
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return sort_r(base, num, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
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}
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EXPORT_SYMBOL(sort);
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