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authorKuan-Wei Chiu <visitorckw@gmail.com>2024-04-07 11:39:04 +0800
committerKent Overstreet <kent.overstreet@linux.dev>2024-04-13 14:33:15 -0400
commit7d47f79a607e0be5ef333a8aa15ddc2fcfc151d3 (patch)
tree5139cd451d139f5c8bf241ccc997bdd12a21e287 /fs/bcachefs/btree_iter.h
parentee1276829da498c92f9c4e42e3d327aaa732fcf3 (diff)
bcachefs: Optimize eytzinger0_sort() with bottom-up heapsort
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> Signed-off-by: Kent Overstreet <kent.overstreet@linux.dev>
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