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linux/fs/bcachefs/eytzinger.c
Kuan-Wei Chiu 0ddb5f0854 bcachefs: Optimize eytzinger0_sort() with bottom-up heapsort
This optimization reduces the average number of comparisons required
from 2*n*log2(n) - 3*n + o(n) to n*log2(n) + 0.37*n + o(n). When n is
sufficiently large, it results in approximately 50% fewer comparisons.

Currently, eytzinger0_sort employs the textbook version of heapsort,
where during the heapify process, each level requires two comparisons
to determine the maximum among three elements. In contrast, the
bottom-up heapsort, during heapify, only compares two children at each
level until reaching a leaf node. Then, it backtracks from the leaf
node to find the correct position. Since heapify typically continues
until very close to the leaf node, the standard heapify requires about
2*log2(n) comparisons, while the bottom-up variant only needs log2(n)
comparisons.

The experimental data presented below is based on an array generated
by get_random_u32().

|   N   | comparisons(old) | comparisons(new) | time(old) | time(new) |
|-------|------------------|------------------|-----------|-----------|
| 10000 |     235381       |     136615       |  25545 us |  20366 us |
| 20000 |     510694       |     293425       |  31336 us |  18312 us |
| 30000 |     800384       |     457412       |  35042 us |  27386 us |
| 40000 |    1101617       |     626831       |  48779 us |  38253 us |
| 50000 |    1409762       |     799637       |  62238 us |  46950 us |
| 60000 |    1721191       |     974521       |  75588 us |  58367 us |
| 70000 |    2038536       |    1152171       |  90823 us |  68778 us |
| 80000 |    2362958       |    1333472       | 104165 us |  78625 us |
| 90000 |    2690900       |    1516065       | 116111 us |  89573 us |
| 100000|    3019413       |    1699879       | 133638 us | 100998 us |

Refs:
  BOTTOM-UP-HEAPSORT, a new variant of HEAPSORT beating, on an average,
  QUICKSORT (if n is not very small)
  Ingo Wegener
  Theoretical Computer Science, 118(1); Pages 81-98, 13 September 1993
  https://doi.org/10.1016/0304-3975(93)90364-Y

Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
Signed-off-by: Kent Overstreet <kent.overstreet@linux.dev>
2024-05-08 17:29:18 -04:00

306 lines
7.9 KiB
C

// SPDX-License-Identifier: GPL-2.0
#include "eytzinger.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: 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 still 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);
}
/*
* 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_r_func_t)0
#define SWAP_WORDS_32 (swap_r_func_t)1
#define SWAP_BYTES (swap_r_func_t)2
#define SWAP_WRAPPER (swap_r_func_t)3
struct wrapper {
cmp_func_t cmp;
swap_func_t swap_func;
};
/*
* 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_r_func_t swap_func, const void *priv)
{
if (swap_func == SWAP_WRAPPER) {
((const struct wrapper *)priv)->swap_func(a, b, (int)size);
return;
}
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, priv);
}
#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 ((const struct wrapper *)priv)->cmp(a, b);
return cmp(a, b, priv);
}
static inline int eytzinger0_do_cmp(void *base, size_t n, size_t size,
cmp_r_func_t cmp_func, const void *priv,
size_t l, size_t r)
{
return do_cmp(base + inorder_to_eytzinger0(l, n) * size,
base + inorder_to_eytzinger0(r, n) * size,
cmp_func, priv);
}
static inline void eytzinger0_do_swap(void *base, size_t n, size_t size,
swap_r_func_t swap_func, const void *priv,
size_t l, size_t r)
{
do_swap(base + inorder_to_eytzinger0(l, n) * size,
base + inorder_to_eytzinger0(r, n) * size,
size, swap_func, priv);
}
void eytzinger0_sort_r(void *base, size_t n, size_t size,
cmp_r_func_t cmp_func,
swap_r_func_t swap_func,
const void *priv)
{
int i, j, k;
/* called from 'sort' without swap function, let's pick the default */
if (swap_func == SWAP_WRAPPER && !((struct wrapper *)priv)->swap_func)
swap_func = NULL;
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;
}
/* heapify */
for (i = n / 2 - 1; i >= 0; --i) {
/* Find the sift-down path all the way to the leaves. */
for (j = i; k = j * 2 + 1, k + 1 < n;)
j = eytzinger0_do_cmp(base, n, size, cmp_func, priv, k, k + 1) > 0 ? k : k + 1;
/* Special case for the last leaf with no sibling. */
if (j * 2 + 2 == n)
j = j * 2 + 1;
/* Backtrack to the correct location. */
while (j != i && eytzinger0_do_cmp(base, n, size, cmp_func, priv, i, j) >= 0)
j = (j - 1) / 2;
/* Shift the element into its correct place. */
for (k = j; j != i;) {
j = (j - 1) / 2;
eytzinger0_do_swap(base, n, size, swap_func, priv, j, k);
}
}
/* sort */
for (i = n - 1; i > 0; --i) {
eytzinger0_do_swap(base, n, size, swap_func, priv, 0, i);
/* Find the sift-down path all the way to the leaves. */
for (j = 0; k = j * 2 + 1, k + 1 < i;)
j = eytzinger0_do_cmp(base, n, size, cmp_func, priv, k, k + 1) > 0 ? k : k + 1;
/* Special case for the last leaf with no sibling. */
if (j * 2 + 2 == i)
j = j * 2 + 1;
/* Backtrack to the correct location. */
while (j && eytzinger0_do_cmp(base, n, size, cmp_func, priv, 0, j) >= 0)
j = (j - 1) / 2;
/* Shift the element into its correct place. */
for (k = j; j;) {
j = (j - 1) / 2;
eytzinger0_do_swap(base, n, size, swap_func, priv, j, k);
}
}
}
void eytzinger0_sort(void *base, size_t n, size_t size,
cmp_func_t cmp_func,
swap_func_t swap_func)
{
struct wrapper w = {
.cmp = cmp_func,
.swap_func = swap_func,
};
return eytzinger0_sort_r(base, n, size, _CMP_WRAPPER, SWAP_WRAPPER, &w);
}
#if 0
#include <linux/slab.h>
#include <linux/random.h>
#include <linux/ktime.h>
static u64 cmp_count;
static int mycmp(const void *a, const void *b)
{
u32 _a = *(u32 *)a;
u32 _b = *(u32 *)b;
cmp_count++;
if (_a < _b)
return -1;
else if (_a > _b)
return 1;
else
return 0;
}
static int test(void)
{
size_t N, i;
ktime_t start, end;
s64 delta;
u32 *arr;
for (N = 10000; N <= 100000; N += 10000) {
arr = kmalloc_array(N, sizeof(u32), GFP_KERNEL);
cmp_count = 0;
for (i = 0; i < N; i++)
arr[i] = get_random_u32();
start = ktime_get();
eytzinger0_sort(arr, N, sizeof(u32), mycmp, NULL);
end = ktime_get();
delta = ktime_us_delta(end, start);
printk(KERN_INFO "time: %lld\n", delta);
printk(KERN_INFO "comparisons: %lld\n", cmp_count);
u32 prev = 0;
eytzinger0_for_each(i, N) {
if (prev > arr[i])
goto err;
prev = arr[i];
}
kfree(arr);
}
return 0;
err:
kfree(arr);
return -1;
}
#endif