• Rick Hudson's avatar
    runtime: redo insert/remove of large spans · 6e9ec141
    Rick Hudson authored
    Currently for spans with up to 1 MBytes (128 pages) we
    maintain an array indexed by the number of pages in the
    span. This is efficient both in terms of space as well
    as time to insert or remove a span of a particular size.
    
    Unfortunately for spans larger than 1 MByte we currently
    place them on a separate linked list. This results in
    O(n) behavior. Now that we are seeing heaps approaching
    100 GBytes n is large enough to be noticed in real programs.
    
    This change replaces the linked list now used with a balanced
    binary tree structure called a treap. A treap is a
    probabilistically balanced tree offering O(logN) behavior for
    inserting and removing spans.
    
    To verify that this approach will work we start with noting
    that only spans with sizes > 1MByte will be put into the treap.
    This means that to support 1 TByte a treap will need at most
    1 million nodes and can ideally be held in a treap with a
    depth of 20. Experiments with adding and removing randomly
    sized spans from the treap seem to result in treaps with
    depths of about twice the ideal or 40. A petabyte would
    require a tree of only twice again that depth again so this
    algorithm should last well into the future.
    
    Fixes #19393
    
    Go1 benchmarks indicate this is basically an overall wash.
    Tue Mar 28 21:29:21 EDT 2017
    name                     old time/op    new time/op    delta
    BinaryTree17-4              2.42s ± 1%     2.42s ± 1%    ~     (p=0.980 n=21+21)
    Fannkuch11-4                3.00s ± 1%     3.18s ± 4%  +6.10%  (p=0.000 n=22+24)
    FmtFprintfEmpty-4          40.5ns ± 1%    40.3ns ± 3%    ~     (p=0.692 n=22+25)
    FmtFprintfString-4         65.9ns ± 3%    64.6ns ± 1%  -1.98%  (p=0.000 n=24+23)
    FmtFprintfInt-4            69.6ns ± 1%    68.0ns ± 7%  -2.30%  (p=0.001 n=21+22)
    FmtFprintfIntInt-4          102ns ± 2%      99ns ± 1%  -3.07%  (p=0.000 n=23+23)
    FmtFprintfPrefixedInt-4     126ns ± 0%     125ns ± 0%  -0.79%  (p=0.000 n=19+17)
    FmtFprintfFloat-4           206ns ± 2%     205ns ± 1%    ~     (p=0.671 n=23+21)
    FmtManyArgs-4               441ns ± 1%     445ns ± 1%  +0.88%  (p=0.000 n=22+23)
    GobDecode-4                5.73ms ± 1%    5.86ms ± 1%  +2.37%  (p=0.000 n=23+22)
    GobEncode-4                4.51ms ± 1%    4.89ms ± 1%  +8.32%  (p=0.000 n=22+22)
    Gzip-4                      197ms ± 0%     202ms ± 1%  +2.75%  (p=0.000 n=23+24)
    Gunzip-4                   32.9ms ± 8%    32.7ms ± 2%    ~     (p=0.466 n=23+24)
    HTTPClientServer-4         57.3µs ± 1%    56.7µs ± 1%  -0.94%  (p=0.000 n=21+22)
    JSONEncode-4               13.8ms ± 1%    13.9ms ± 2%  +1.14%  (p=0.000 n=22+23)
    JSONDecode-4               47.4ms ± 1%    48.1ms ± 1%  +1.49%  (p=0.000 n=23+23)
    Mandelbrot200-4            3.92ms ± 0%    3.92ms ± 1%  +0.21%  (p=0.000 n=22+22)
    GoParse-4                  2.89ms ± 1%    2.87ms ± 1%  -0.68%  (p=0.000 n=21+22)
    RegexpMatchEasy0_32-4      73.6ns ± 1%    72.0ns ± 2%  -2.15%  (p=0.000 n=21+22)
    RegexpMatchEasy0_1K-4       173ns ± 1%     173ns ± 1%    ~     (p=0.847 n=22+24)
    RegexpMatchEasy1_32-4      71.9ns ± 1%    69.8ns ± 1%  -2.99%  (p=0.000 n=23+20)
    RegexpMatchEasy1_1K-4       314ns ± 1%     308ns ± 1%  -1.91%  (p=0.000 n=22+23)
    RegexpMatchMedium_32-4      106ns ± 0%     105ns ± 1%  -0.58%  (p=0.000 n=19+21)
    RegexpMatchMedium_1K-4     34.3µs ± 1%    34.3µs ± 1%    ~     (p=0.871 n=23+22)
    RegexpMatchHard_32-4       1.67µs ± 1%    1.67µs ± 7%    ~     (p=0.224 n=22+23)
    RegexpMatchHard_1K-4       51.5µs ± 1%    50.4µs ± 1%  -1.99%  (p=0.000 n=22+23)
    Revcomp-4                   383ms ± 1%     415ms ± 0%  +8.51%  (p=0.000 n=22+22)
    Template-4                 51.5ms ± 1%    51.5ms ± 1%    ~     (p=0.555 n=20+23)
    TimeParse-4                 279ns ± 2%     277ns ± 1%  -0.95%  (p=0.000 n=24+22)
    TimeFormat-4                294ns ± 1%     296ns ± 1%  +0.58%  (p=0.003 n=24+23)
    [Geo mean]                 43.7µs         43.8µs       +0.32%
    
    name                     old speed      new speed      delta
    GobDecode-4               134MB/s ± 1%   131MB/s ± 1%  -2.32%  (p=0.000 n=23+22)
    GobEncode-4               170MB/s ± 1%   157MB/s ± 1%  -7.68%  (p=0.000 n=22+22)
    Gzip-4                   98.7MB/s ± 0%  96.1MB/s ± 1%  -2.68%  (p=0.000 n=23+24)
    Gunzip-4                  590MB/s ± 7%   593MB/s ± 2%    ~     (p=0.466 n=23+24)
    JSONEncode-4              141MB/s ± 1%   139MB/s ± 2%  -1.13%  (p=0.000 n=22+23)
    JSONDecode-4             40.9MB/s ± 1%  40.3MB/s ± 0%  -1.47%  (p=0.000 n=23+23)
    GoParse-4                20.1MB/s ± 1%  20.2MB/s ± 1%  +0.69%  (p=0.000 n=21+22)
    RegexpMatchEasy0_32-4     435MB/s ± 1%   444MB/s ± 2%  +2.21%  (p=0.000 n=21+22)
    RegexpMatchEasy0_1K-4    5.89GB/s ± 1%  5.89GB/s ± 1%    ~     (p=0.439 n=22+24)
    RegexpMatchEasy1_32-4     445MB/s ± 1%   459MB/s ± 1%  +3.06%  (p=0.000 n=23+20)
    RegexpMatchEasy1_1K-4    3.26GB/s ± 1%  3.32GB/s ± 1%  +1.97%  (p=0.000 n=22+23)
    RegexpMatchMedium_32-4   9.40MB/s ± 1%  9.44MB/s ± 1%  +0.43%  (p=0.000 n=23+21)
    RegexpMatchMedium_1K-4   29.8MB/s ± 1%  29.8MB/s ± 1%    ~     (p=0.826 n=23+22)
    RegexpMatchHard_32-4     19.1MB/s ± 1%  19.1MB/s ± 7%    ~     (p=0.233 n=22+23)
    RegexpMatchHard_1K-4     19.9MB/s ± 1%  20.3MB/s ± 1%  +2.03%  (p=0.000 n=22+23)
    Revcomp-4                 664MB/s ± 1%   612MB/s ± 0%  -7.85%  (p=0.000 n=22+22)
    Template-4               37.6MB/s ± 1%  37.7MB/s ± 1%    ~     (p=0.558 n=20+23)
    [Geo mean]                134MB/s        133MB/s       -0.76%
    Tue Mar 28 22:16:54 EDT 2017
    
    Change-Id: I4a4f5c2b53d3fb85ef76c98522d3ed5cf8ae5b7e
    Reviewed-on: https://go-review.googlesource.com/38732Reviewed-by: 's avatarRuss Cox <rsc@golang.org>
    6e9ec141
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