// 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, @b: pointers to the elements
* @size: 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, @b: pointers to the elements
* @size: 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, @b: pointers to the elements
* @size: 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(sort);
