// SPDX-License-Identifier: GPL-2.0
/*
- * A fast, small, non-recursive O(nlog n) sort for the Linux kernel
+ * A fast, small, non-recursive O(n log n) sort for the Linux kernel
*
- * Jan 23 2005 Matt Mackall <mpm@selenic.com>
+ * 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/export.h>
#include <linux/sort.h>
-static int alignment_ok(const void *base, int align)
+/**
+ * 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)
{
- return IS_ENABLED(CONFIG_HAVE_EFFICIENT_UNALIGNED_ACCESS) ||
- ((unsigned long)base & (align - 1)) == 0;
+ 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;
}
-static void u32_swap(void *a, void *b, int size)
+/**
+ * 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)
{
- u32 t = *(u32 *)a;
- *(u32 *)a = *(u32 *)b;
- *(u32 *)b = t;
+ do {
+ u32 t = *(u32 *)(a + (n -= 4));
+ *(u32 *)(a + n) = *(u32 *)(b + n);
+ *(u32 *)(b + n) = t;
+ } while (n);
}
-static void u64_swap(void *a, void *b, int size)
+/**
+ * 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)
{
- u64 t = *(u64 *)a;
- *(u64 *)a = *(u64 *)b;
- *(u64 *)b = t;
+ 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);
}
-static void generic_swap(void *a, void *b, int size)
+/**
+ * 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)
{
- char t;
-
do {
- t = *(char *)a;
- *(char *)a++ = *(char *)b;
- *(char *)b++ = t;
- } while (--size > 0);
+ 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;
}
/**
* @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 optimized to your element type.
+ * 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
- * qsort is about 20% faster on average, it suffers from exploitable
+ * 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 */
- int i = (num/2 - 1) * size, n = num * size, c, r;
+ 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 (size == 4 && alignment_ok(base, 4))
- swap_func = u32_swap;
- else if (size == 8 && alignment_ok(base, 8))
- swap_func = u64_swap;
+ 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 = generic_swap;
+ swap_func = SWAP_BYTES;
}
- /* heapify */
- for ( ; i >= 0; i -= size) {
- for (r = i; r * 2 + size < n; r = c) {
- c = r * 2 + size;
- if (c < n - size &&
- cmp_func(base + c, base + c + size) < 0)
- c += size;
- if (cmp_func(base + r, base + c) >= 0)
- break;
- swap_func(base + r, base + c, size);
- }
- }
+ /*
+ * 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;
- /* sort */
- for (i = n - size; i > 0; i -= size) {
- swap_func(base, base + i, size);
- for (r = 0; r * 2 + size < i; r = c) {
- c = r * 2 + size;
- if (c < i - size &&
- cmp_func(base + c, base + c + size) < 0)
- c += size;
- if (cmp_func(base + r, base + c) >= 0)
- break;
- swap_func(base + r, base + c, size);
+ /*
+ * 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);
projects / linux-2.6-microblaze.git / blobdiff