Messages in this thread Patch in this message | ![/](/images/icornerl.gif) | | Date | Sun, 7 Apr 2024 10:54:46 +0800 | From | Kuan-Wei Chiu <> | Subject | Re: [PATCH] bcachefs: Optimize eytzinger0_sort() with bottom-up heapsort |
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On Sat, Apr 06, 2024 at 10:05:44PM -0400, Kent Overstreet wrote: > 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@gmail.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. >
I rewrote the testing part as follows:
u32 prev = 0; eytzinger0_for_each(i, N) { if (prev > arr[i]) goto err; prev = arr[i]; }
And the test still passed.
Thanks, Kuan-Wei > > > > 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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