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 <[email protected]>
---
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/[email protected]/
[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;
}
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
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 <[email protected]>
> ---
>
> 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/[email protected]/
> [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
>
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 <[email protected]>
> > ---
> >
> > 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/[email protected]/
> > [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
> >
On Sun, Apr 07, 2024 at 10:54:46AM +0800, Kuan-Wei Chiu wrote:
> 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 <[email protected]>
> > > ---
> > >
> > > 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/[email protected]/
> > > [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.
Great, can you include that? I'd be fine with it #if 0'd out, I just
want it there.
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 <[email protected]>
---
Changes in v2:
- Add the testing code to the source code and wrap it with #if 0.
fs/bcachefs/eytzinger.c | 105 +++++++++++++++++++++++++++++++++-------
1 file changed, 88 insertions(+), 17 deletions(-)
diff --git a/fs/bcachefs/eytzinger.c b/fs/bcachefs/eytzinger.c
index 0f955c3c76a7..2eaffe37b5e7 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;
+ /* 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;
- if (c + 1 < n &&
- 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 == n)
+ 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 != i && eytzinger0_do_cmp(base, n, size, cmp_func, priv, i, 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 != 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);
}
}
}
@@ -232,3 +242,64 @@ void eytzinger0_sort(void *base, size_t n, size_t size,
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
--
2.34.1
On Sun, Apr 07, 2024 at 11:39:04AM +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 <[email protected]>
Thanks - applied