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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 |
|
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Linux kernel
============
There are several guides for kernel developers and users. These guides can
be rendered in a number of formats, like HTML and PDF. Please read
Documentation/admin-guide/README.rst first.
In order to build the documentation, use ``make htmldocs`` or
``make pdfdocs``. The formatted documentation can also be read online at:
https://www.kernel.org/doc/html/latest/
There are various text files in the Documentation/ subdirectory,
several of them using the reStructuredText markup notation.
Please read the Documentation/process/changes.rst file, as it contains the
requirements for building and running the kernel, and information about
the problems which may result by upgrading your kernel.