[PFC]: hash instrumentation

Chuck Lever (cel@monkey.org)
Wed, 7 Apr 1999 15:49:36 -0400 (EDT)

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[PFC] = patch for comments - not a bug fix or for general use

i've attached a diff to this message that contains the hash
instrumentation i'm using to analyze and improve hash functions. i'd like
to instrument a couple of other hashes (dentry, inode, fib), and create a
new directory in /proc called /proc/cache, with files for each of the
important caches. these may not contain the histogram information, since
it's just for testing, but they might contain important statistics about
hash performance, for example.

here's some sample output (from /var/log/messages) to show what
information you might be able to gather from the hash instrumentation:

for the page cache:

Apr 7 15:08:50 pillbox kernel: Total pages in hash: 4079 total buckets:
2048
Apr 7 15:08:50 pillbox kernel: hash table histogram:
Apr 7 15:08:50 pillbox kernel: size: 0 buckets: 379 pages: 0
Apr 7 15:08:50 pillbox kernel: size: 1 buckets: 462 pages: 462
Apr 7 15:08:50 pillbox kernel: size: 2 buckets: 507 pages: 1014
Apr 7 15:08:50 pillbox kernel: size: 3 buckets: 385 pages: 1155
Apr 7 15:08:50 pillbox kernel: size: 4 buckets: 178 pages: 712
Apr 7 15:08:50 pillbox kernel: size: 5 buckets: 94 pages: 470
Apr 7 15:08:50 pillbox kernel: size: 6 buckets: 36 pages: 216
Apr 7 15:08:50 pillbox kernel: size: 7 buckets: 6 pages: 42
Apr 7 15:08:50 pillbox kernel: size: 8 buckets: 1 pages: 8
Apr 7 15:08:50 pillbox kernel: size: 9 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: size: 10 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: size: 11 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: size: 12 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: size: 13 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: size: 14 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: size: 15 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: size:>15 buckets: 0 pages: 0
Apr 7 15:08:50 pillbox kernel: Max bucket size: 8
Apr 7 15:08:50 pillbox kernel: Total lookups: 58933 pages found: 52044
(hit rate: 88%)
Apr 7 15:08:50 pillbox kernel: find_page loops: 53950 loops/lookup:
915/1000

notice that the bucket sizes are nicely distributed, and that most of the
buckets are used. loops/lookup is really the number that matters here,
since it provides a good indication of how much average effort is required
to find a given page. loops/lookup is the average number of times
__find_page (or find_buffer, below) had to loop during a lookup operation.

the histogram table is organized so that each row represents buckets of a
given size. for instance, the row for empty buckets is "size:0" and the
number of buckets that were empty is 379. the number of buckets that
contained only 2 pages is 507, and there were 1014 pages stored in buckets
that only contained 2 pages. this allows us to clearly see the bucket
size distribution, and to easily tell when there are lots of large or
empty buckets (both bad situations).

here's the buffer cache:

Apr 7 15:08:50 pillbox kernel: total buffers in hash table: 2149
Apr 7 15:08:50 pillbox kernel: total buckets: 32768 largest: 59
Apr 7 15:08:50 pillbox kernel: times find_buffer looped: 53900
loops/lookup: 874/1000
Apr 7 15:08:50 pillbox kernel: hash table histogram:
Apr 7 15:08:50 pillbox kernel: size: 0 buckets: 31941 buffers: 0
Apr 7 15:08:50 pillbox kernel: size: 1 buckets: 648 buffers: 648
Apr 7 15:08:50 pillbox kernel: size: 2 buckets: 50 buffers: 100
Apr 7 15:08:50 pillbox kernel: size: 3 buckets: 26 buffers: 78
Apr 7 15:08:50 pillbox kernel: size: 4 buckets: 8 buffers: 32
Apr 7 15:08:50 pillbox kernel: size: 5 buckets: 16 buffers: 80
Apr 7 15:08:50 pillbox kernel: size: 6 buckets: 17 buffers: 102
Apr 7 15:08:50 pillbox kernel: size: 7 buckets: 18 buffers: 126
Apr 7 15:08:50 pillbox kernel: size: 8 buckets: 12 buffers: 96
Apr 7 15:08:50 pillbox kernel: size: 9 buckets: 3 buffers: 27
Apr 7 15:08:50 pillbox kernel: size: 10 buckets: 5 buffers: 50
Apr 7 15:08:50 pillbox kernel: size: 11 buckets: 4 buffers: 44
Apr 7 15:08:50 pillbox kernel: size: 12 buckets: 1 buffers: 12
Apr 7 15:08:50 pillbox kernel: size: 13 buckets: 0 buffers: 0
Apr 7 15:08:50 pillbox kernel: size: 14 buckets: 2 buffers: 28
Apr 7 15:08:50 pillbox kernel: size: 15 buckets: 0 buffers: 0
Apr 7 15:08:50 pillbox kernel: size:>15 buckets: 17 buffers: 726

the buffer hash function doesn't work well: bucket sizes are not nicely
distributed, there is a huge number of empty buckets, and there are more
than a few buckets that contain lots of buffers. this is just after the
system was booted, but after some file system intensive activity, we have
this:

page hash:

Apr 7 15:36:20 pillbox kernel: Total pages in hash: 21854 total buckets:
2048
Apr 7 15:36:20 pillbox kernel: hash table histogram:
Apr 7 15:36:20 pillbox kernel: size: 0 buckets: 0 pages: 0
Apr 7 15:36:20 pillbox kernel: size: 1 buckets: 0 pages: 0
Apr 7 15:36:20 pillbox kernel: size: 2 buckets: 3 pages: 6
Apr 7 15:36:20 pillbox kernel: size: 3 buckets: 4 pages: 12
Apr 7 15:36:20 pillbox kernel: size: 4 buckets: 20 pages: 80
Apr 7 15:36:20 pillbox kernel: size: 5 buckets: 60 pages: 300
Apr 7 15:36:20 pillbox kernel: size: 6 buckets: 76 pages: 456
Apr 7 15:36:20 pillbox kernel: size: 7 buckets: 131 pages: 917
Apr 7 15:36:20 pillbox kernel: size: 8 buckets: 198 pages: 1584
Apr 7 15:36:20 pillbox kernel: size: 9 buckets: 247 pages: 2223
Apr 7 15:36:20 pillbox kernel: size: 10 buckets: 261 pages: 2610
Apr 7 15:36:20 pillbox kernel: size: 11 buckets: 284 pages: 3124
Apr 7 15:36:20 pillbox kernel: size: 12 buckets: 224 pages: 2688
Apr 7 15:36:20 pillbox kernel: size: 13 buckets: 185 pages: 2405
Apr 7 15:36:20 pillbox kernel: size: 14 buckets: 148 pages: 2072
Apr 7 15:36:20 pillbox kernel: size: 15 buckets: 82 pages: 1230
Apr 7 15:36:20 pillbox kernel: size:>15 buckets: 125 pages: 1427
Apr 7 15:36:20 pillbox kernel: Max bucket size: 22
Apr 7 15:36:20 pillbox kernel: Total lookups: 5129003 pages found:
4590496 (hit rate: 89%)
Apr 7 15:36:20 pillbox kernel: find_page loops: 28371900 loops/lookup:
507/1000

the loops/lookup is pretty low (less than one is good) and the hash
distribution is still nicely shaped. it's clear that the hash table is
too small, though. for buffers:

Apr 7 15:36:20 pillbox kernel: total buffers in hash table: 1767
Apr 7 15:36:20 pillbox kernel: total buckets: 32768 largest: 25
Apr 7 15:36:20 pillbox kernel: times find_buffer looped: 2314427
loops/lookup: 1078/1000
Apr 7 15:36:20 pillbox kernel: hash table histogram:
Apr 7 15:36:20 pillbox kernel: size: 0 buckets: 31866 buffers: 0
Apr 7 15:36:20 pillbox kernel: size: 1 buckets: 687 buffers: 687
Apr 7 15:36:20 pillbox kernel: size: 2 buckets: 109 buffers: 218
Apr 7 15:36:20 pillbox kernel: size: 3 buckets: 19 buffers: 57
Apr 7 15:36:20 pillbox kernel: size: 4 buckets: 11 buffers: 44
Apr 7 15:36:20 pillbox kernel: size: 5 buckets: 15 buffers: 75
Apr 7 15:36:20 pillbox kernel: size: 6 buckets: 9 buffers: 54
Apr 7 15:36:20 pillbox kernel: size: 7 buckets: 9 buffers: 63
Apr 7 15:36:20 pillbox kernel: size: 8 buckets: 4 buffers: 32
Apr 7 15:36:20 pillbox kernel: size: 9 buckets: 7 buffers: 63
Apr 7 15:36:20 pillbox kernel: size: 10 buckets: 4 buffers: 40
Apr 7 15:36:20 pillbox kernel: size: 11 buckets: 5 buffers: 55
Apr 7 15:36:20 pillbox kernel: size: 12 buckets: 4 buffers: 48
Apr 7 15:36:20 pillbox kernel: size: 13 buckets: 6 buffers: 78
Apr 7 15:36:20 pillbox kernel: size: 14 buckets: 1 buffers: 14
Apr 7 15:36:20 pillbox kernel: size: 15 buckets: 1 buffers: 15
Apr 7 15:36:20 pillbox kernel: size:>15 buckets: 11 buffers: 224

for buffers the story is quite different. there's still a huge number of
empty buckets, and the size distribution is practically flat.
loops/lookup is greater than one.

- Chuck Lever

--
corporate:	<chuckl@netscape.com>
personal:	<chucklever@netscape.net> or <cel@monkey.org>


The Linux Scalability project:
	http://www.citi.umich.edu/projects/citi-netscape/


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