22a241ccb2
This uses fewer comparisons than the previous code (approaching half as
many for large random inputs), but produces identical results; it
actually performs the exact same series of swap operations.
Specifically, it reduces the average number of compares from
2*n*log2(n) - 3*n + o(n)
to
n*log2(n) + 0.37*n + o(n).
This is still 1.63*n worse than glibc qsort() which manages n*log2(n) -
1.26*n, but at least the leading coefficient is correct.
Standard heapsort, when sifting down, performs two comparisons per
level: one to find the greater child, and a second to see if the current
node should be exchanged with that child.
Bottom-up heapsort observes that it's better to postpone the second
comparison and search for the leaf where -infinity would be sent to,
then search back *up* for the current node's destination.
Since sifting down usually proceeds to the leaf level (that's where half
the nodes are), this does O(1) second comparisons rather than log2(n).
That saves a lot of (expensive since Spectre) indirect function calls.
The one time it's worse than the previous code is if there are large
numbers of duplicate keys, when the top-down algorithm is O(n) and
bottom-up is O(n log n). For distinct keys, it's provably always
better, doing 1.5*n*log2(n) + O(n) in the worst case.
(The code is not significantly more complex. This patch also merges the
heap-building and -extracting sift-down loops, resulting in a net code
size savings.)
x86-64 code size 885 -> 767 bytes (-118)
(I see the checkpatch complaint about "else if (n -= size)". The
alternative is significantly uglier.)
Link: http://lkml.kernel.org/r/2de8348635a1a421a72620677898c7fd5bd4b19d.1552704200.git.lkml@sdf.org
Signed-off-by: George Spelvin <lkml@sdf.org>
Acked-by: Andrey Abramov <st5pub@yandex.ru>
Acked-by: Rasmus Villemoes <linux@rasmusvillemoes.dk>
Reviewed-by: Andy Shevchenko <andriy.shevchenko@linux.intel.com>
Cc: Daniel Wagner <daniel.wagner@siemens.com>
Cc: Dave Chinner <dchinner@redhat.com>
Cc: Don Mullis <don.mullis@gmail.com>
Cc: Geert Uytterhoeven <geert@linux-m68k.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
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| Documentation | ||
| LICENSES | ||
| arch | ||
| block | ||
| certs | ||
| crypto | ||
| drivers | ||
| fs | ||
| include | ||
| init | ||
| ipc | ||
| kernel | ||
| lib | ||
| mm | ||
| net | ||
| samples | ||
| scripts | ||
| security | ||
| sound | ||
| tools | ||
| usr | ||
| virt | ||
| .clang-format | ||
| .cocciconfig | ||
| .get_maintainer.ignore | ||
| .gitattributes | ||
| .gitignore | ||
| .mailmap | ||
| COPYING | ||
| CREDITS | ||
| Kbuild | ||
| Kconfig | ||
| MAINTAINERS | ||
| Makefile | ||
| README | ||
README
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 Restructured Text 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.