// 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_inlinestatic 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);} typedef int (*cmp_func_t)(const void *, const void *);typedef int (*cmp_r_func_t)(const void *, const void *, const void *);#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 ((cmp_func_t)(priv))(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_inlinestatic 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,	    int (*cmp_func)(const void *, const void *, const void *),	    void (*swap_func)(void *, void *, int size),	    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; 	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 = 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);		}	}}EXPORT_SYMBOL(sort_r); void sort(void *base, size_t num, size_t size,	  int (*cmp_func)(const void *, const void *),	  void (*swap_func)(void *, void *, int size)){	return sort_r(base, num, size, _CMP_WRAPPER, swap_func, cmp_func);}EXPORT_SYMBOL(sort);