tree be179915300e6d6ea61c8458c7e1ccb764065ed4
parent d6a2eedfddcded92c8f9b0ac022a99c4134696b0
author Don Mullis <don.mullis@gmail.com> 1267825395 -0800
committer Linus Torvalds <torvalds@linux-foundation.org> 1267903595 -0800

lib: more scalable list_sort()

XFS and UBIFS can pass long lists to list_sort(); this alternative
implementation scales better, reaching ~3x performance gain when list
length exceeds the L2 cache size.

Stand-alone program timings were run on a Core 2 duo L1=32KB L2=4MB,
gcc-4.4, with flags extracted from an Ubuntu kernel build.  Object size is
581 bytes compared to 455 for Mark J.  Roberts' code.

Worst case for either implementation is a list length just over a power of
two, and to roughly the same degree, so here are timing results for a
range of 2^N+1 lengths.  List elements were 16 bytes each including malloc
overhead; initial order was random.

                      time (msec)
                      Tatham-Roberts
                      |       generic-Mullis-v2
loop_count  length    |       |    ratio
4000000       2     206     294    1.427
2000000       3     176     227    1.289
1000000       5     199     172    0.864
 500000       9     235     178    0.757
 250000      17     243     182    0.748
 125000      33     261     196    0.750
  62500      65     277     209    0.754
  31250     129     292     219    0.75
  15625     257     317     235    0.741
   7812     513     340     252    0.741
   3906    1025     362     267    0.737
   1953    2049     388     283    0.729  ~ L1 size
    976    4097     556     323    0.580
    488    8193     678     361    0.532
    244   16385     773     395    0.510
    122   32769     844     418    0.495
     61   65537     917     454    0.495
     30  131073    1128     543    0.481
     15  262145    2355     869    0.369  ~ L2 size
      7  524289    5597    1714    0.306
      3 1048577    6218    2022    0.325

Mark's code does not actually implement the usual or generic mergesort,
but rather a variant from Simon Tatham described here:

    http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html

Simon's algorithm performs O(log N) passes over the entire input list,
doing merges of sublists that double in size on each pass.  The generic
algorithm instead merges pairs of equal length lists as early as possible,
in recursive order.  For either algorithm, the elements that extend the
list beyond power-of-two length are a special case, handled as nearly as
possible as a "rounding-up" to a full POT.

Some intuition for the locality of reference implications of merge order
may be gotten by watching this animation:

    http://www.sorting-algorithms.com/merge-sort

Simon's algorithm requires only O(1) extra space rather than the generic
algorithm's O(log N), but in my non-recursive implementation the actual
O(log N) data is merely a vector of ~20 pointers, which I've put on the
stack.

Long-running list_sort() calls: If the list passed in may be long, or the
client's cmp() callback function is slow, the client's cmp() may
periodically invoke cond_resched() to voluntarily yield the CPU.  All
inner loops of list_sort() call back to cmp().

Stability of the sort: distinct elements that compare equal emerge from
the sort in the same order as with Mark's code, for simple test cases.  A
boot-time test is provided to verify this and other correctness
requirements.

A kernel that uses drm.ko appears to run normally with this change; I have
no suitable hardware to similarly test the use by UBIFS.

[akpm@linux-foundation.org: style tweaks, fix comment, make list_sort_test __init]
Signed-off-by: Don Mullis <don.mullis@gmail.com>
Cc: Dave Airlie <airlied@redhat.com>
Cc: Andi Kleen <andi@firstfloor.org>
Cc: Dave Chinner <david@fromorbit.com>
Cc: Artem Bityutskiy <dedekind@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>