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Date: Sat, 6 Apr 2024 22:05:44 -0400
From: Kent Overstreet <kent.overstreet@...ux.dev>
To: Kuan-Wei Chiu <visitorckw@...il.com>
Cc: bfoster@...hat.com, jserv@...s.ncku.edu.tw,
linux-bcachefs@...r.kernel.org, linux-kernel@...r.kernel.org
Subject: Re: [PATCH] bcachefs: Optimize eytzinger0_sort() with bottom-up
heapsort
On Sun, Apr 07, 2024 at 09:33:49AM +0800, Kuan-Wei Chiu wrote:
> 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 is the same as the patch I submitted previously [1]. Since we
> decided not to move eytzinger.h to generic library code, I resubmitted
> this patch.
>
> This patch has undergone unit testing and micro benchmarking using the
> following code [2].
>
> [1]: https://lore.kernel.org/lkml/20240121153649.2733274-2-visitorckw@gmail.com/
> [2]:
> static u64 cmp_count = 0;
>
> 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, 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;
> }
Use eytzinger0_for_each() to just compare every element against the
previous element, and check in the test code.
>
> kfree(arr);
> }
> return 0;
>
> err:
> kfree(arr);
> return -1;
> }
>
> fs/bcachefs/eytzinger.c | 50 ++++++++++++++++++++++++-----------------
> 1 file changed, 30 insertions(+), 20 deletions(-)
>
> diff --git a/fs/bcachefs/eytzinger.c b/fs/bcachefs/eytzinger.c
> index 0f955c3c76a7..9a99a1410d12 100644
> --- a/fs/bcachefs/eytzinger.c
> +++ b/fs/bcachefs/eytzinger.c
> @@ -171,7 +171,7 @@ void eytzinger0_sort_r(void *base, size_t n, size_t size,
> swap_r_func_t swap_func,
> const void *priv)
> {
> - int i, c, r;
> + 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)
> @@ -188,17 +188,22 @@ void eytzinger0_sort_r(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 &&
> - eytzinger0_do_cmp(base, n, size, cmp_func, priv, c, c + 1) < 0)
> - c++;
> -
> - if (eytzinger0_do_cmp(base, n, size, cmp_func, priv, r, c) >= 0)
> - break;
> -
> - eytzinger0_do_swap(base, n, size, swap_func, priv, r, c);
> + /* 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);
> }
> }
>
> @@ -206,17 +211,22 @@ void eytzinger0_sort_r(void *base, size_t n, size_t size,
> for (i = n - 1; i > 0; --i) {
> eytzinger0_do_swap(base, n, size, swap_func, priv, 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 = eytzinger0_do_cmp(base, n, size, cmp_func, priv, k, k + 1) > 0 ? k : k + 1;
>
> - if (c + 1 < i &&
> - eytzinger0_do_cmp(base, n, size, cmp_func, priv, c, c + 1) < 0)
> - c++;
> + /* Special case for the last leaf with no sibling. */
> + if (j * 2 + 2 == i)
> + j = j * 2 + 1;
>
> - if (eytzinger0_do_cmp(base, n, size, cmp_func, priv, r, c) >= 0)
> - break;
> + /* Backtrack to the correct location. */
> + while (j && eytzinger0_do_cmp(base, n, size, cmp_func, priv, 0, j) >= 0)
> + j = (j - 1) / 2;
>
> - eytzinger0_do_swap(base, n, size, swap_func, priv, r, c);
> + /* 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);
> }
> }
> }
> --
> 2.34.1
>
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