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Message-Id: <20240121153649.2733274-2-visitorckw@gmail.com>
Date: Sun, 21 Jan 2024 23:36:45 +0800
From: Kuan-Wei Chiu <visitorckw@...il.com>
To: colyli@...e.de,
kent.overstreet@...ux.dev
Cc: bfoster@...hat.com,
jserv@...s.ncku.edu.tw,
linux-bcache@...r.kernel.org,
linux-kernel@...r.kernel.org,
linux-bcachefs@...r.kernel.org,
Kuan-Wei Chiu <visitorckw@...il.com>
Subject: [PATCH 1/5] bcachefs: Optimize eytzinger0_sort() using 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@...il.com>
---
This patch has undergone unit testing and micro benchmarking using the
following code [1].
[1]:
static long long int cmp_count = 0;
static int mycmp(const void *a, const void *b, size_t size)
{
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, L, R;
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);
for (int i = 0; i < N; i++) {
L = 2 * i + 1;
R = 2 * i + 2;
if (L < N && arr[i] < arr[L])
goto err;
if (R < N && arr[i] > arr[R])
goto err;
}
kfree(arr);
}
return 0;
err:
kfree(arr);
return -1;
}
fs/bcachefs/util.c | 50 +++++++++++++++++++++++++++-------------------
1 file changed, 30 insertions(+), 20 deletions(-)
diff --git a/fs/bcachefs/util.c b/fs/bcachefs/util.c
index c2ef7cddaa4f..bbc83b43162e 100644
--- a/fs/bcachefs/util.c
+++ b/fs/bcachefs/util.c
@@ -911,7 +911,7 @@ void eytzinger0_sort(void *base, size_t n, size_t size,
int (*cmp_func)(const void *, const void *, size_t),
void (*swap_func)(void *, void *, size_t))
{
- int i, c, r;
+ int i, j, k;
if (!swap_func) {
if (size == 4 && alignment_ok(base, 4))
@@ -924,17 +924,22 @@ void eytzinger0_sort(void *base, size_t n, size_t size,
/* heapify */
for (i = n / 2 - 1; i >= 0; --i) {
- for (r = i; r * 2 + 1 < n; r = c) {
- c = r * 2 + 1;
-
- if (c + 1 < n &&
- do_cmp(base, n, size, cmp_func, c, c + 1) < 0)
- c++;
-
- if (do_cmp(base, n, size, cmp_func, r, c) >= 0)
- break;
-
- do_swap(base, n, size, swap_func, r, c);
+ /* Find the sift-down path all the way to the leaves. */
+ for (j = i; k = j * 2 + 1, k + 1 < n;)
+ j = do_cmp(base, n, size, cmp_func, 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 && do_cmp(base, n, size, cmp_func, i, j) >= 0)
+ j = (j - 1) / 2;
+
+ /* Shift the element into its correct place. */
+ for (k = j; j != i;) {
+ j = (j - 1) / 2;
+ do_swap(base, n, size, swap_func, j, k);
}
}
@@ -942,17 +947,22 @@ void eytzinger0_sort(void *base, size_t n, size_t size,
for (i = n - 1; i > 0; --i) {
do_swap(base, n, size, swap_func, 0, i);
- for (r = 0; r * 2 + 1 < i; r = c) {
- c = r * 2 + 1;
+ /* Find the sift-down path all the way to the leaves. */
+ for (j = 0; k = j * 2 + 1, k + 1 < i;)
+ j = do_cmp(base, n, size, cmp_func, k, k + 1) > 0 ? k : k + 1;
- if (c + 1 < i &&
- do_cmp(base, n, size, cmp_func, c, c + 1) < 0)
- c++;
+ /* Special case for the last leaf with no sibling. */
+ if (j * 2 + 2 == i)
+ j = j * 2 + 1;
- if (do_cmp(base, n, size, cmp_func, r, c) >= 0)
- break;
+ /* Backtrack to the correct location. */
+ while (j && do_cmp(base, n, size, cmp_func, 0, j) >= 0)
+ j = (j - 1) / 2;
- do_swap(base, n, size, swap_func, r, c);
+ /* Shift the element into its correct place. */
+ for (k = j; j;) {
+ j = (j - 1) / 2;
+ do_swap(base, n, size, swap_func, j, k);
}
}
}
--
2.25.1
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