Messages in this thread | | | Date | Sun, 7 Apr 2024 00:12:22 -0400 | From | Kent Overstreet <> | Subject | Re: [PATCH v2] bcachefs: Optimize eytzinger0_sort() with bottom-up heapsort |
| |
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 <visitorckw@gmail.com>
Thanks - applied
| |