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.
