作者
José Valim <jose(点)valim(在)gmail(点)com>
状态
最终/24.0 已在 OTP 版本 24 中实现
类型
标准跟踪
创建时间
2019年9月18日

EEP 50:基于映射的集合实现 #

摘要 #

此 EEP 提出了基于映射的集合实现和一组 BIF,旨在在 Erlang/OTP 中提供一个事实上的集合实现。

动机 #

为了今天在 Erlang/OTP 中高效地使用集合,必须考虑三种不同的选择

  • ordsets
  • gb_sets
  • 使用映射作为集合(例如 cerl_sets

例如,如果您希望执行并集/交集/差集操作,ordsets 通常是最有效的。对于单独的查找,首选 gb_sets 和“映射作为集合”,尽管后者在 Erlang/OTP 中没有官方 API。如果需要混合配置,最佳选择会变得模糊。请注意,还有一个 sets 模块,但它很少是一个可行的选项。

当前集合的格局与 Erlang/OTP 17 之前的字典格局没有太大差别。幸运的是,一旦添加了 mapsmaps 就成为 Erlang 中事实上的字典。其他类似字典的模块在有限的情况下可能会表现更好,但 maps 在许多场景中提供了最佳的性能,并且是一个合理的起点(直到出现基准测试和性能分析的需求——如果真的会出现的话)。

此 EEP 的目标是提出一个基于映射的集合解决方案,并提供一组 BIF,这将为开发人员提供一个通常可以在 Erlang/OTP 中被视为主要集合实现的集合实现。

原理 #

字典和集合实现往往并肩而行。例如 ordsetsorddictgb_treesgb_sets。这是因为您可以将集合中的元素视为字典中的键,而您不关心键的值。

鉴于我们已经将字典实现为映射,我们是否可以拥有基于映射的集合?答案是肯定的,并且有两种方法。第一种方法是提供一种用 C 实现的本机数据结构,并具有自己的语法。这种方法的优点是内存使用量较低,但会对语言和运行时产生很大的影响。因此,这不是我们在这里要采用的方法。

第二种方法,也是此 EEP 所倡导的方法,是在映射之上实现 sets,就像 cerl_sets 所做的那样。在这种情况下,集合元素是映射中的键,而值是空列表(我们选择空列表是因为它们很容易序列化)。

使用“映射作为集合”在插入、添加和删除集合元素方面提供了良好的性能特征,比所有其他实现都快。但是,在内存使用方面,“映射作为集合”使用的内存几乎是 ordsets 的两倍(尽管请注意,集合操作本身最终可能会使用更少的内存)。与 gb_sets 相比,“映射作为集合”总体上使用的内存更少。

但是,“映射作为集合”在并集、交集和差集操作中能像 ordsets 一样快吗?

好消息是:**这对于并集已经成立**,它等效于 maps:merge/2。基准测试在附录中提供,我们可以得出以下结论

  1. 在对整数元素进行并集时,映射和 ordsets 所需的时间大致相同,除了必须从小映射转换为大映射的情况外,映射略微领先

  2. 在对元组元素进行并集时,映射始终更快,有时快 2 到 4 倍,除了必须从小映射转换为大映射的情况外。这是意料之中的,比较项的成本越高,ordsets 的成本就越高

这意味着,如果我们可以基于映射实现交集和差集,那么它很可能比 ordsets 更有效,因为交集和差集不会出现映射大小调整的问题。

使用小映射和混合映射的交集概念验证已经完成,结果是积极的(请参见附录中的基准测试)。我们还可以看到新的交集始终比 cerl_sets 快。不幸的是,由于此 EEP 作者缺乏 C 专业知识,因此没有两个大映射之间交集的基准测试。应该验证的假设是,相交大映射将比相交大 ordsets 快。

考虑到 maps:merge/2 中看到的结果以及映射大小调整不会发生在交集上这一事实,此假设很可能会被证明是正确的。

因此,如果我们的目标是使 maps 在这些操作中像 ordsets 一样快,我们需要实现新的 BIF。

规范 #

对于检查、添加和删除元素,“映射作为集合”通常比现有的集合实现更有效。但是,在以下操作中,它们比 ordsets

  • from_list/1
  • is_subset/2
  • is_disjoint/2
  • intersection/2
  • subtract/2

因此,如果我们想要一个事实上的集合实现,则必须将上述函数实现为 BIF。前三个与纯 Erlang 实现相比仅提供部分加速,但后两个操作将通过 NIF 提供大幅提升。后两个操作也是最难实现的。

通过上述更改,“映射作为集合”中唯一不会像“ordsets”一样快或更快的操作是 to_listfold,因为 ordsets 在内部是列表。

假设上述功能被验证为性能更高(至少对于交集和差集而言),并且有兴趣提供此功能,那么最后一个问题是:此功能应该如何公开?

“映射作为集合”的可能 API #

  1. 增强映射模块

    如果没有兴趣向 OTP 添加新模块,可以增强“映射”模块以具有基于集合的操作。在这些情况下,只比较键。值可以来自第一个或第二个映射。

    虽然这种方法会提高性能,但 maps 中的 intersection/2subtract/2 API 相当笨拙。一种替代方法是以 key 前缀为这些操作添加前缀,例如 keyintersection,以清楚地表明它们是关于键的交集。但也许更好的方法是定义一个单独的模块。

  2. 添加 mapsets 模块

    mapsets 模块提供基于映射的集合。该集合基于映射的事实是公共 API 的一部分(即,它们不是不透明类型),就像 ordsets 一样。每个键的值都是空列表,以确保可以轻松地序列化集合。

    这个新模块将有 5 个 BIF

    • mapsets:from_list/1
    • mapsets:intersection/2
    • mapsets:is_subset/2
    • mapsets:is_disjoint/2
    • mapsets:subtract/2

    其余的 API 将在映射 API 之上实现。

  3. 更改 sets 模块

    与上述类似的另一个选择是利用 sets 类型是不透明的这一事实,并用“映射作为集合”替换其实现。这种方法的优点是,今天使用 sets 的每个人都会获得性能升级,并且我们将避免向 Erlang/OTP 添加新模块。毕竟,总是存在这样一种风险:通过添加统一所有三个现有选项的第四个选项,我们最终只会得到四个选项。

    这种方法的缺点是,尽管 sets 数据结构是不透明的,但开发人员可能已在其他地方对其进行了序列化,因此仍然必须支持现有数据结构。这意味着我们首先需要修改 sets 模块以同时支持旧集合和新的“映射作为集合”。对旧数据结构的支持只能在未来的版本中删除。

    Erlang/OTP 技术委员会更倾向于此选项。sets 模块将有两个新函数 sets:new/1sets:from_list/2,它们接受 version 选项。如果给定了 {version, 2},则将创建作为映射的集合。sets 模块中的其余 API 被设计为可用于新旧集合。版本 2 将在 Erlang/OTP 26 中成为默认版本。

实施步骤 #

实施应分三个步骤完成

  1. 更新 sets 模块以支持返回“映射作为集合”的版本标志

  2. 从 Erlang/OTP 中删除 cerl_sets

  3. 将相关操作优化为 BIF

版权 #

本文档已置于公共领域。

[VimVar]: <> “ vim: set fileencoding=utf-8 expandtab shiftwidth=4 softtabstop=4: “

附录:并集基准测试结果 #

整数集合的并集 #

Operating System: macOS
CPU Information: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Number of Available Cores: 8
Available memory: 16 GB
Elixir 1.9.0
Erlang 23-master

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
Estimated total run time: 8.40 min

##### With input a1 Interspersed (5) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           4.18 M      239.50 ns ±13926.78%           0 ns
   1000 ns
3 ordsets:union        2.73 M      365.68 ns  ±8833.12%           0 ns
   1000 ns
2 gb_sets:union        0.99 M     1008.99 ns  ±2897.13%        1000 ns
   2000 ns

Comparison:
1 maps:merge           4.18 M
3 ordsets:union        2.73 M - 1.53x slower +126.19 ns
2 gb_sets:union        0.99 M - 4.21x slower +769.49 ns

##### With input a2 Interspersed (10) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           3.60 M      277.93 ns  ±9122.84%           0 ns
   1000 ns
3 ordsets:union        1.93 M      517.34 ns  ±5920.40%           0 ns
   1000 ns
2 gb_sets:union        0.62 M     1624.47 ns  ±2115.84%        1000 ns
   3000 ns

Comparison:
1 maps:merge           3.60 M
3 ordsets:union        1.93 M - 1.86x slower +239.41 ns
2 gb_sets:union        0.62 M - 5.84x slower +1346.54 ns

##### With input a3 Interspersed (30) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union     1012.27 K        0.99 μs  ±4048.88%           1 μs
      2 μs
1 maps:merge         318.99 K        3.13 μs   ±558.61%           3 μs
      7 μs
2 gb_sets:union      270.93 K        3.69 μs   ±222.80%           3 μs
     12 μs

Comparison:
3 ordsets:union     1012.27 K
1 maps:merge         318.99 K - 3.17x slower +2.15 μs
2 gb_sets:union      270.93 K - 3.74x slower +2.70 μs

##### With input a4 Interspersed (50) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge        1149.76 K        0.87 μs  ±3450.02%           1 μs
      2 μs
3 ordsets:union      584.09 K        1.71 μs  ±1716.00%           1 μs
      4 μs
2 gb_sets:union      146.62 K        6.82 μs   ±311.32%           6 μs
     25 μs

Comparison:
1 maps:merge        1149.76 K
3 ordsets:union      584.09 K - 1.97x slower +0.84 μs
2 gb_sets:union      146.62 K - 7.84x slower +5.95 μs

##### With input a5 Interspersed (1000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge          71.57 K       13.97 μs   ±154.74%          12 μs
     44 μs
3 ordsets:union       33.29 K       30.04 μs   ±134.28%          25 μs
     92 μs
2 gb_sets:union        8.36 K      119.56 μs    ±52.83%         106 μs
    255 μs

Comparison:
1 maps:merge          71.57 K
3 ordsets:union       33.29 K - 2.15x slower +16.07 μs
2 gb_sets:union        8.36 K - 8.56x slower +105.58 μs

##### With input a6 Interspersed (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           275.98        3.62 ms    ±36.94%        2.75 ms
   7.26 ms
3 ordsets:union        247.19        4.05 ms    ±14.63%        4.01 ms
   5.39 ms
2 gb_sets:union         43.70       22.88 ms    ±28.56%       20.66 ms
  44.84 ms

Comparison:
1 maps:merge           275.98
3 ordsets:union        247.19 - 1.12x slower +0.42 ms
2 gb_sets:union         43.70 - 6.32x slower +19.26 ms

##### With input b1 Half-left (5) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union        5.14 M      194.71 ns  ±2814.44%           0 ns
   1000 ns
1 maps:merge           4.80 M      208.36 ns ±20621.17%           0 ns
   1000 ns
2 gb_sets:union        1.48 M      673.48 ns  ±4924.77%        1000 ns
   1000 ns

Comparison:
3 ordsets:union        5.14 M
1 maps:merge           4.80 M - 1.07x slower +13.65 ns
2 gb_sets:union        1.48 M - 3.46x slower +478.77 ns

##### With input b2 Half-left (10) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           4.42 M      226.29 ns  ±9473.44%           0 ns
   1000 ns
3 ordsets:union        3.73 M      268.01 ns ±12800.39%           0 ns
   1000 ns
2 gb_sets:union        0.87 M     1144.30 ns  ±2389.89%        1000 ns
   2000 ns

Comparison:
1 maps:merge           4.42 M
3 ordsets:union        3.73 M - 1.18x slower +41.72 ns
2 gb_sets:union        0.87 M - 5.06x slower +918.01 ns

##### With input b3 Half-left (30) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           2.64 M      378.92 ns ±12298.14%           0 ns
   1000 ns
3 ordsets:union        1.70 M      589.31 ns  ±7472.62%           0 ns
   1000 ns
2 gb_sets:union        0.43 M     2326.42 ns   ±393.28%        2000 ns
   4000 ns

Comparison:
1 maps:merge           2.64 M
3 ordsets:union        1.70 M - 1.56x slower +210.39 ns
2 gb_sets:union        0.43 M - 6.14x slower +1947.49 ns

##### With input b4 Half-left (50) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union     1365.15 K        0.73 μs  ±3249.86%           1 μs
      1 μs
1 maps:merge         587.14 K        1.70 μs  ±1709.70%           1 μs
      3 μs
2 gb_sets:union      254.37 K        3.93 μs   ±510.57%           3 μs
     16 μs

Comparison:
3 ordsets:union     1365.15 K
1 maps:merge         587.14 K - 2.33x slower +0.97 μs
2 gb_sets:union      254.37 K - 5.37x slower +3.20 μs

##### With input b5 Half-left (1000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge         130.95 K        7.64 μs    ±44.63%           7 μs
     25 μs
3 ordsets:union      112.42 K        8.90 μs   ±271.51%           8 μs
     34 μs
2 gb_sets:union       14.89 K       67.17 μs    ±81.58%          58 μs
 167.75 μs

Comparison:
1 maps:merge         130.95 K
3 ordsets:union      112.42 K - 1.16x slower +1.26 μs
2 gb_sets:union       14.89 K - 8.80x slower +59.54 μs

##### With input b6 Half-left (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           736.54        1.36 ms    ±13.50%        1.30 ms
   2.17 ms
3 ordsets:union        424.33        2.36 ms    ±20.47%        2.28 ms
   3.81 ms
2 gb_sets:union        111.06        9.00 ms    ±14.00%        8.64 ms
  14.87 ms

Comparison:
1 maps:merge           736.54
3 ordsets:union        424.33 - 1.74x slower +1.00 ms
2 gb_sets:union        111.06 - 6.63x slower +7.65 ms

##### With input c1 Half-right (5) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union        5.39 M      185.61 ns  ±3347.98%           0 ns
   1000 ns
1 maps:merge           4.44 M      224.99 ns ±18210.87%           0 ns
   1000 ns
2 gb_sets:union        1.38 M      726.62 ns  ±5484.65%        1000 ns
   2000 ns

Comparison:
3 ordsets:union        5.39 M
1 maps:merge           4.44 M - 1.21x slower +39.37 ns
2 gb_sets:union        1.38 M - 3.91x slower +541.01 ns

##### With input c2 Half-right (10) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           4.50 M      222.20 ns  ±6200.17%           0 ns
   1000 ns
3 ordsets:union        3.66 M      273.47 ns ±11368.54%           0 ns
   1000 ns
2 gb_sets:union        0.91 M     1097.73 ns  ±2497.65%        1000 ns
   2000 ns

Comparison:
1 maps:merge           4.50 M
3 ordsets:union        3.66 M - 1.23x slower +51.26 ns
2 gb_sets:union        0.91 M - 4.94x slower +875.52 ns

##### With input c3 Half-right (30) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           2.88 M      346.75 ns ±11287.26%           0 ns
   1000 ns
3 ordsets:union        1.87 M      534.45 ns  ±5864.66%           0 ns
   1000 ns
2 gb_sets:union        0.42 M     2353.46 ns   ±409.72%        2000 ns
   5000 ns

Comparison:
1 maps:merge           2.88 M
3 ordsets:union        1.87 M - 1.54x slower +187.69 ns
2 gb_sets:union        0.42 M - 6.79x slower +2006.70 ns

##### With input c4 Half-right (50) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union     1405.29 K        0.71 μs  ±4860.25%           1 μs
      2 μs
1 maps:merge         541.91 K        1.85 μs  ±1461.20%           2 μs
      3 μs
2 gb_sets:union      248.12 K        4.03 μs   ±526.17%           3 μs
     17 μs

Comparison:
3 ordsets:union     1405.29 K
1 maps:merge         541.91 K - 2.59x slower +1.13 μs
2 gb_sets:union      248.12 K - 5.66x slower +3.32 μs

##### With input c5 Half-right (1000) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union      117.05 K        8.54 μs   ±180.01%           8 μs
     32 μs
1 maps:merge         106.28 K        9.41 μs   ±706.19%           8 μs
     28 μs
2 gb_sets:union       14.62 K       68.38 μs    ±69.45%          59 μs
    149 μs

Comparison:
3 ordsets:union      117.05 K
1 maps:merge         106.28 K - 1.10x slower +0.87 μs
2 gb_sets:union       14.62 K - 8.00x slower +59.84 μs

##### With input c6 Half-right (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           447.90        2.23 ms    ±42.50%        1.81 ms
   6.07 ms
3 ordsets:union        312.45        3.20 ms    ±35.75%        2.92 ms
   7.20 ms
2 gb_sets:union        110.13        9.08 ms    ±14.75%        8.72 ms
  16.01 ms

Comparison:
1 maps:merge           447.90
3 ordsets:union        312.45 - 1.43x slower +0.97 ms
2 gb_sets:union        110.13 - 4.07x slower +6.85 ms

##### With input d1 Equal (5) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           4.03 M      248.00 ns ±13008.64%           0 ns
   1000 ns
3 ordsets:union        3.41 M      293.08 ns ±11881.46%           0 ns
   1000 ns
2 gb_sets:union        1.34 M      748.45 ns  ±5426.61%        1000 ns
   2000 ns

Comparison:
1 maps:merge           4.03 M
3 ordsets:union        3.41 M - 1.18x slower +45.08 ns
2 gb_sets:union        1.34 M - 3.02x slower +500.44 ns

##### With input d2 Equal (10) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union        3.33 M      300.31 ns  ±5298.85%           0 ns
   1000 ns
1 maps:merge           2.81 M      355.61 ns ±14326.68%           0 ns
   1000 ns
2 gb_sets:union        0.75 M     1337.84 ns  ±2488.47%        1000 ns
   4000 ns

Comparison:
3 ordsets:union        3.33 M
1 maps:merge           2.81 M - 1.18x slower +55.30 ns
2 gb_sets:union        0.75 M - 4.45x slower +1037.53 ns

##### With input d3 Equal (30) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           2.25 M      443.46 ns  ±8688.55%           0 ns
   1000 ns
3 ordsets:union        1.46 M      683.82 ns  ±3817.58%        1000 ns
   1000 ns
2 gb_sets:union        0.37 M     2686.18 ns   ±483.99%        2000 ns
   9000 ns

Comparison:
1 maps:merge           2.25 M
3 ordsets:union        1.46 M - 1.54x slower +240.36 ns
2 gb_sets:union        0.37 M - 6.06x slower +2242.72 ns

##### With input d4 Equal (50) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           1.50 M      668.83 ns   ±132.24%        1000 ns
   1000 ns
3 ordsets:union        1.04 M      960.02 ns  ±4458.67%        1000 ns
   2000 ns
2 gb_sets:union        0.22 M     4523.49 ns   ±196.98%        4000 ns
  18000 ns

Comparison:
1 maps:merge           1.50 M
3 ordsets:union        1.04 M - 1.44x slower +291.19 ns
2 gb_sets:union        0.22 M - 6.76x slower +3854.66 ns

##### With input d5 Equal (1000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge          81.92 K       12.21 μs    ±57.31%          11 μs
     32 μs
3 ordsets:union       77.39 K       12.92 μs   ±129.75%          12 μs
     39 μs
2 gb_sets:union       12.72 K       78.63 μs    ±43.08%          70 μs
    174 μs

Comparison:
1 maps:merge          81.92 K
3 ordsets:union       77.39 K - 1.06x slower +0.71 μs
2 gb_sets:union       12.72 K - 6.44x slower +66.43 μs

##### With input d6 Equal (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           646.20        1.55 ms    ±18.21%        1.45 ms
   2.86 ms
3 ordsets:union        305.88        3.27 ms    ±16.73%        3.22 ms
   4.79 ms
2 gb_sets:union         96.06       10.41 ms    ±18.09%        9.72 ms
  17.41 ms

Comparison:
1 maps:merge           646.20
3 ordsets:union        305.88 - 2.11x slower +1.72 ms
2 gb_sets:union         96.06 - 6.73x slower +8.86 ms

元组整数集合的并集 #

Operating System: macOS
CPU Information: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Number of Available Cores: 8
Available memory: 16 GB
Elixir 1.9.0
Erlang 23-master

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
Estimated total run time: 8.40 min

##### With input a1 Interspersed (5) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           2.93 M      341.36 ns  ±2603.07%           0 ns
   1000 ns
3 ordsets:union        1.62 M      616.04 ns  ±4989.81%           0 ns
   1000 ns
2 gb_sets:union        0.82 M     1219.38 ns  ±2533.38%        1000 ns
   2000 ns

Comparison:
1 maps:merge           2.93 M
3 ordsets:union        1.62 M - 1.80x slower +274.68 ns
2 gb_sets:union        0.82 M - 3.57x slower +878.02 ns

##### With input a2 Interspersed (10) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           2.02 M      494.89 ns  ±2798.11%           0 ns
   1000 ns
3 ordsets:union        1.04 M      963.72 ns  ±2195.45%        1000 ns
   2000 ns
2 gb_sets:union        0.50 M     2012.64 ns  ±1226.89%        2000 ns
   4000 ns

Comparison:
1 maps:merge           2.02 M
3 ordsets:union        1.04 M - 1.95x slower +468.83 ns
2 gb_sets:union        0.50 M - 4.07x slower +1517.75 ns

##### With input a3 Interspersed (30) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union      408.22 K        2.45 μs   ±828.38%           2 μs
      4 μs
1 maps:merge         234.27 K        4.27 μs   ±330.95%           4 μs
     10 μs
2 gb_sets:union      189.97 K        5.26 μs   ±643.32%           5 μs
     18 μs

Comparison:
3 ordsets:union      408.22 K
1 maps:merge         234.27 K - 1.74x slower +1.82 μs
2 gb_sets:union      189.97 K - 2.15x slower +2.81 μs

##### With input a4 Interspersed (50) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge         767.56 K        1.30 μs  ±1279.19%           1 μs
      2 μs
3 ordsets:union      246.12 K        4.06 μs   ±267.03%           4 μs
     14 μs
2 gb_sets:union      108.33 K        9.23 μs   ±255.73%           8 μs
     27 μs

Comparison:
1 maps:merge         767.56 K
3 ordsets:union      246.12 K - 3.12x slower +2.76 μs
2 gb_sets:union      108.33 K - 7.09x slower +7.93 μs

##### With input a5 Interspersed (1000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge          47.61 K       21.00 μs   ±196.69%          19 μs
     59 μs
3 ordsets:union       12.38 K       80.76 μs    ±53.12%          73 μs
    193 μs
2 gb_sets:union        6.04 K      165.68 μs    ±30.74%         152 μs
    309 μs

Comparison:
1 maps:merge          47.61 K
3 ordsets:union       12.38 K - 3.84x slower +59.75 μs
2 gb_sets:union        6.04 K - 7.89x slower +144.67 μs

##### With input a6 Interspersed (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           210.63        4.75 ms    ±35.35%        3.77 ms
   9.58 ms
3 ordsets:union         74.84       13.36 ms    ±17.83%       12.73 ms
  18.51 ms
2 gb_sets:union         54.06       18.50 ms    ±14.28%       17.83 ms
  24.21 ms

Comparison:
1 maps:merge           210.63
3 ordsets:union         74.84 - 2.81x slower +8.61 ms
2 gb_sets:union         54.06 - 3.90x slower +13.75 ms

##### With input b1 Half-left (5) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           4.49 M      222.57 ns  ±1774.31%           0 ns
   1000 ns
3 ordsets:union        3.33 M      300.45 ns  ±6349.54%           0 ns
   1000 ns
2 gb_sets:union        1.46 M      683.85 ns  ±2344.50%        1000 ns
   1000 ns

Comparison:
1 maps:merge           4.49 M
3 ordsets:union        3.33 M - 1.35x slower +77.88 ns
2 gb_sets:union        1.46 M - 3.07x slower +461.29 ns

##### With input b2 Half-left (10) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           2.48 M      402.60 ns  ±9495.69%           0 ns
   1000 ns
3 ordsets:union        2.30 M      435.32 ns  ±1123.50%           0 ns
   1000 ns
2 gb_sets:union        0.76 M     1318.82 ns   ±818.75%        1000 ns
   2000 ns

Comparison:
1 maps:merge           2.48 M
3 ordsets:union        2.30 M - 1.08x slower +32.73 ns
2 gb_sets:union        0.76 M - 3.28x slower +916.23 ns

##### With input b3 Half-left (30) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           1.54 M      648.33 ns  ±2884.79%           0 ns
   1000 ns
3 ordsets:union        1.09 M      921.12 ns   ±734.80%        1000 ns
   2000 ns
2 gb_sets:union        0.37 M     2728.75 ns   ±554.08%        2000 ns
   6000 ns

Comparison:
1 maps:merge           1.54 M
3 ordsets:union        1.09 M - 1.42x slower +272.79 ns
2 gb_sets:union        0.37 M - 4.21x slower +2080.42 ns

##### With input b4 Half-left (50) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union      734.80 K        1.36 μs   ±978.11%           1 μs
      3 μs
1 maps:merge         439.62 K        2.27 μs  ±1429.61%           2 μs
      5 μs
2 gb_sets:union      224.47 K        4.45 μs   ±213.29%           4 μs
     15 μs

Comparison:
3 ordsets:union      734.80 K
1 maps:merge         439.62 K - 1.67x slower +0.91 μs
2 gb_sets:union      224.47 K - 3.27x slower +3.09 μs

##### With input b5 Half-left (1000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge          76.01 K       13.16 μs   ±104.36%          12 μs
     35 μs
3 ordsets:union       45.29 K       22.08 μs   ±125.57%          20 μs
     60 μs
2 gb_sets:union       13.42 K       74.53 μs    ±44.00%          68 μs
    164 μs

Comparison:
1 maps:merge          76.01 K
3 ordsets:union       45.29 K - 1.68x slower +8.93 μs
2 gb_sets:union       13.42 K - 5.66x slower +61.37 μs

##### With input b6 Half-left (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           530.32        1.89 ms    ±18.53%        1.77 ms
   3.40 ms
3 ordsets:union        139.97        7.14 ms    ±17.91%        7.01 ms
  11.23 ms
2 gb_sets:union         91.51       10.93 ms    ±12.31%       10.34 ms
  15.62 ms

Comparison:
1 maps:merge           530.32
3 ordsets:union        139.97 - 3.79x slower +5.26 ms
2 gb_sets:union         91.51 - 5.80x slower +9.04 ms

##### With input c1 Half-right (5) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           4.46 M      224.32 ns  ±1730.97%           0 ns
   1000 ns
3 ordsets:union        3.78 M      264.68 ns  ±3293.90%           0 ns
   1000 ns
2 gb_sets:union        1.52 M      658.44 ns  ±1819.22%        1000 ns
   1000 ns

Comparison:
1 maps:merge           4.46 M
3 ordsets:union        3.78 M - 1.18x slower +40.37 ns
2 gb_sets:union        1.52 M - 2.94x slower +434.13 ns

##### With input c2 Half-right (10) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union        2.36 M      424.51 ns  ±2870.39%           0 ns
   1000 ns
1 maps:merge           2.27 M      441.04 ns ±11548.99%           0 ns
   1000 ns
2 gb_sets:union        0.80 M     1248.21 ns   ±948.08%        1000 ns
   2000 ns

Comparison:
3 ordsets:union        2.36 M
1 maps:merge           2.27 M - 1.04x slower +16.53 ns
2 gb_sets:union        0.80 M - 2.94x slower +823.70 ns

##### With input c3 Half-right (30) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           1.53 M      654.58 ns  ±2879.82%        1000 ns
   1000 ns
3 ordsets:union        1.13 M      885.52 ns  ±2213.29%        1000 ns
   2000 ns
2 gb_sets:union        0.37 M     2675.20 ns   ±502.40%        2000 ns
   5000 ns

Comparison:
1 maps:merge           1.53 M
3 ordsets:union        1.13 M - 1.35x slower +230.94 ns
2 gb_sets:union        0.37 M - 4.09x slower +2020.62 ns

##### With input c4 Half-right (50) #####
Name                      ips        average  deviation         median
    99th %
3 ordsets:union      747.48 K        1.34 μs  ±1222.85%           1 μs
      3 μs
1 maps:merge         433.42 K        2.31 μs  ±1493.25%           2 μs
      4 μs
2 gb_sets:union      223.83 K        4.47 μs   ±283.66%           4 μs
     13 μs

Comparison:
3 ordsets:union      747.48 K
1 maps:merge         433.42 K - 1.72x slower +0.97 μs
2 gb_sets:union      223.83 K - 3.34x slower +3.13 μs

##### With input c5 Half-right (1000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge          66.00 K       15.15 μs   ±321.69%          14 μs
     41 μs
3 ordsets:union       44.62 K       22.41 μs   ±767.12%          20 μs
     60 μs
2 gb_sets:union       13.20 K       75.74 μs    ±41.33%          70 μs
    161 μs

Comparison:
1 maps:merge          66.00 K
3 ordsets:union       44.62 K - 1.48x slower +7.26 μs
2 gb_sets:union       13.20 K - 5.00x slower +60.59 μs

##### With input c6 Half-right (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           428.32        2.33 ms    ±28.88%        2.06 ms
   4.05 ms
3 ordsets:union        146.62        6.82 ms    ±18.71%        6.60 ms
  10.79 ms
2 gb_sets:union         91.45       10.93 ms    ±13.58%       10.27 ms
  15.80 ms

Comparison:
1 maps:merge           428.32
3 ordsets:union        146.62 - 2.92x slower +4.49 ms
2 gb_sets:union         91.45 - 4.68x slower +8.60 ms

##### With input d1 Equal (5) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           3.61 M      276.63 ns  ±3338.58%           0 ns
   1000 ns
3 ordsets:union        2.42 M      414.07 ns  ±3326.82%           0 ns
   1000 ns
2 gb_sets:union        1.26 M      792.13 ns  ±1546.56%        1000 ns
   2000 ns

Comparison:
1 maps:merge           3.61 M
3 ordsets:union        2.42 M - 1.50x slower +137.45 ns
2 gb_sets:union        1.26 M - 2.86x slower +515.50 ns

##### With input d2 Equal (10) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           2.15 M      464.77 ns  ±8475.08%           0 ns
   1000 ns
3 ordsets:union        1.88 M      531.65 ns   ±493.39%        1000 ns
   1000 ns
2 gb_sets:union        0.69 M     1459.20 ns  ±1113.96%        1000 ns
   3000 ns

Comparison:
1 maps:merge           2.15 M
3 ordsets:union        1.88 M - 1.14x slower +66.89 ns
2 gb_sets:union        0.69 M - 3.14x slower +994.43 ns

##### With input d3 Equal (30) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge        1364.57 K        0.73 μs  ±4056.53%           1 μs
      1 μs
3 ordsets:union      742.74 K        1.35 μs  ±1193.06%           1 μs
      2 μs
2 gb_sets:union      307.17 K        3.26 μs   ±527.79%           3 μs
      8 μs

Comparison:
1 maps:merge        1364.57 K
3 ordsets:union      742.74 K - 1.84x slower +0.61 μs
2 gb_sets:union      307.17 K - 4.44x slower +2.52 μs

##### With input d4 Equal (50) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge         816.34 K        1.22 μs   ±168.59%           1 μs
      2 μs
3 ordsets:union      451.06 K        2.22 μs  ±1119.27%           2 μs
      4 μs
2 gb_sets:union      184.50 K        5.42 μs   ±200.77%           5 μs
     19 μs

Comparison:
1 maps:merge         816.34 K
3 ordsets:union      451.06 K - 1.81x slower +0.99 μs
2 gb_sets:union      184.50 K - 4.42x slower +4.19 μs

##### With input d5 Equal (1000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge          46.22 K       21.63 μs    ±39.65%          20 μs
     53 μs
3 ordsets:union       26.20 K       38.17 μs    ±63.50%          35 μs
    101 μs
2 gb_sets:union       10.24 K       97.66 μs    ±36.11%          90 μs
    199 μs

Comparison:
1 maps:merge          46.22 K
3 ordsets:union       26.20 K - 1.76x slower +16.53 μs
2 gb_sets:union       10.24 K - 4.51x slower +76.03 μs

##### With input d6 Equal (100000) #####
Name                      ips        average  deviation         median
    99th %
1 maps:merge           440.81        2.27 ms    ±12.79%        2.17 ms
   3.48 ms
3 ordsets:union        126.12        7.93 ms    ±26.40%        7.11 ms
  13.85 ms
2 gb_sets:union         73.86       13.54 ms    ±18.78%       12.89 ms
  19.27 ms

Comparison:
1 maps:merge           440.81
3 ordsets:union        126.12 - 3.50x slower +5.66 ms
2 gb_sets:union         73.86 - 5.97x slower +11.27 ms

附录:交集基准测试结果 #

整数集合的交集 #

Operating System: macOS
CPU Information: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Number of Available Cores: 8
Available memory: 16 GB
Elixir 1.9.0
Erlang 23-master

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
Estimated total run time: 6.53 min

##### With input a1 Interspersed (5) #####
Name                               ips        average  deviation   median       99th %
1 mapsets:intersection          5.64 M      177.31 ns  ±8960.73%     0 ns      1000 ns
3 ordsets:intersection          4.58 M      218.18 ns  ±1955.05%     0 ns      1000 ns
2 gb_sets:intersection          1.85 M      541.24 ns  ±3690.38%     0 ns      1000 ns
0 cerl_sets:intersection        1.81 M      551.00 ns  ±6378.03%     0 ns      1000 ns

Comparison:
1 mapsets:intersection          5.64 M
3 ordsets:intersection          4.58 M - 1.23x slower +40.87 ns
2 gb_sets:intersection          1.85 M - 3.05x slower +363.93 ns
0 cerl_sets:intersection        1.81 M - 3.11x slower +373.69 ns

##### With input a2 Interspersed (10) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          3.87 M      258.37 ns  ±8156.88%     0 ns     1000 ns
3 ordsets:intersection          3.25 M      307.69 ns   ±995.12%     0 ns     1000 ns
0 cerl_sets:intersection        1.35 M      742.45 ns  ±4916.42%  1000 ns     1000 ns
2 gb_sets:intersection          1.20 M      833.71 ns  ±3535.59%  1000 ns     1000 ns

Comparison:
1 mapsets:intersection          3.87 M
3 ordsets:intersection          3.25 M - 1.19x slower +49.32 ns
0 cerl_sets:intersection        1.35 M - 2.87x slower +484.09 ns
2 gb_sets:intersection          1.20 M - 3.23x slower +575.34 ns

##### With input a3 Interspersed (30) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          2.37 M        0.42 μs  ±7530.28%     0 μs        1 μs
3 ordsets:intersection          1.57 M        0.64 μs   ±571.54%     1 μs        1 μs
0 cerl_sets:intersection        0.63 M        1.60 μs  ±1704.57%     1 μs        3 μs
2 gb_sets:intersection          0.57 M        1.74 μs  ±1508.42%     2 μs        3 μs

Comparison:
1 mapsets:intersection          2.37 M
3 ordsets:intersection          1.57 M - 1.51x slower +0.21 μs
0 cerl_sets:intersection        0.63 M - 3.79x slower +1.17 μs
2 gb_sets:intersection          0.57 M - 4.13x slower +1.32 μs

##### With input b1 Half-left (5) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          7.81 M      128.06 ns  ±3031.39%     0 ns     1000 ns
3 ordsets:intersection          6.10 M      163.95 ns   ±819.87%     0 ns     1000 ns
2 gb_sets:intersection          1.91 M      524.17 ns  ±3574.70%     0 ns     1000 ns
0 cerl_sets:intersection        1.73 M      578.18 ns  ±5060.91%     0 ns     1000 ns

Comparison:
1 mapsets:intersection          7.81 M
3 ordsets:intersection          6.10 M - 1.28x slower +35.89 ns
2 gb_sets:intersection          1.91 M - 4.09x slower +396.11 ns
0 cerl_sets:intersection        1.73 M - 4.51x slower +450.12 ns

##### With input b2 Half-left (10) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          5.34 M      187.35 ns  ±6435.27%     0 ns     1000 ns
3 ordsets:intersection          3.50 M      285.53 ns  ±8907.47%     0 ns     1000 ns
0 cerl_sets:intersection        1.25 M      801.68 ns  ±2618.59%  1000 ns     1000 ns
2 gb_sets:intersection          1.15 M      865.97 ns  ±3771.19%  1000 ns     1000 ns

Comparison:
1 mapsets:intersection          5.34 M
3 ordsets:intersection          3.50 M - 1.52x slower +98.18 ns
0 cerl_sets:intersection        1.25 M - 4.28x slower +614.33 ns
2 gb_sets:intersection          1.15 M - 4.62x slower +678.63 ns

##### With input b3 Half-left (30) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          3.12 M        0.32 μs ±10505.28%     0 μs        1 μs
3 ordsets:intersection          1.79 M        0.56 μs  ±5943.47%     0 μs        1 μs
0 cerl_sets:intersection        0.60 M        1.66 μs  ±1650.01%     1 μs        3 μs
2 gb_sets:intersection          0.57 M        1.77 μs  ±1510.44%     2 μs        3 μs

Comparison:
1 mapsets:intersection          3.12 M
3 ordsets:intersection          1.79 M - 1.74x slower +0.24 μs
0 cerl_sets:intersection        0.60 M - 5.17x slower +1.34 μs
2 gb_sets:intersection          0.57 M - 5.51x slower +1.45 μs

##### With input b4 Half-left (50) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          1.41 M        0.71 μs  ±4451.88%     1 μs        1 μs
3 ordsets:intersection          1.32 M        0.76 μs  ±4422.37%     1 μs        1 μs
2 gb_sets:intersection          0.37 M        2.72 μs   ±719.29%     2 μs        5 μs
0 cerl_sets:intersection        0.31 M        3.26 μs   ±464.70%     3 μs        5 μs

Comparison:
1 mapsets:intersection          1.41 M
3 ordsets:intersection          1.32 M - 1.07x slower +0.0487 μs
2 gb_sets:intersection          0.37 M - 3.82x slower +2.01 μs
0 cerl_sets:intersection        0.31 M - 4.59x slower +2.55 μs

##### With input c1 Halt-right (5) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          8.50 M      117.64 ns  ±3751.50%     0 ns     1000 ns
3 ordsets:intersection          4.96 M      201.70 ns  ±1008.33%     0 ns     1000 ns
0 cerl_sets:intersection        2.66 M      375.86 ns  ±7893.27%     0 ns     1000 ns
2 gb_sets:intersection          1.99 M      501.60 ns  ±5740.59%     0 ns     1000 ns

Comparison:
1 mapsets:intersection          8.50 M
3 ordsets:intersection          4.96 M - 1.71x slower +84.06 ns
0 cerl_sets:intersection        2.66 M - 3.20x slower +258.22 ns
2 gb_sets:intersection          1.99 M - 4.26x slower +383.96 ns

##### With input c2 Halt-right (10) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          5.61 M      178.32 ns  ±6353.45%     0 ns     1000 ns
3 ordsets:intersection          3.27 M      305.53 ns  ±8831.03%     0 ns     1000 ns
0 cerl_sets:intersection        1.61 M      619.53 ns  ±5512.50%     0 ns     1000 ns
2 gb_sets:intersection          1.20 M      830.39 ns  ±3587.38%  1000 ns     1000 ns

Comparison:
1 mapsets:intersection          5.61 M
3 ordsets:intersection          3.27 M - 1.71x slower +127.21 ns
0 cerl_sets:intersection        1.61 M - 3.47x slower +441.21 ns
2 gb_sets:intersection          1.20 M - 4.66x slower +652.07 ns

##### With input c3 Halt-right (30) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          3.02 M        0.33 μs ±10877.75%     0 μs        1 μs
3 ordsets:intersection          1.76 M        0.57 μs  ±6736.07%     0 μs        1 μs
0 cerl_sets:intersection        0.83 M        1.20 μs  ±2066.14%     1 μs        2 μs
2 gb_sets:intersection          0.56 M        1.80 μs  ±1442.53%     2 μs        3 μs

Comparison:
1 mapsets:intersection          3.02 M
3 ordsets:intersection          1.76 M - 1.71x slower +0.24 μs
0 cerl_sets:intersection        0.83 M - 3.61x slower +0.87 μs
2 gb_sets:intersection          0.56 M - 5.41x slower +1.46 μs

##### With input c4 Half-right (50) #####
Name                               ips        average  deviation   median      99th %
3 ordsets:intersection          1.42 M        0.70 μs  ±4101.38%     1 μs        1 μs
1 mapsets:intersection          1.31 M        0.77 μs  ±5155.14%     1 μs        1 μs
0 cerl_sets:intersection        0.48 M        2.07 μs  ±1105.13%     2 μs        3 μs
2 gb_sets:intersection          0.37 M        2.69 μs   ±793.20%     2 μs        5 μs

Comparison:
3 ordsets:intersection          1.42 M
1 mapsets:intersection          1.31 M - 1.09x slower +0.0618 μs
0 cerl_sets:intersection        0.48 M - 2.95x slower +1.37 μs
2 gb_sets:intersection          0.37 M - 3.82x slower +1.98 μs

##### With input d1 Equal (5) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          4.61 M      216.84 ns  ±4985.98%     0 ns     1000 ns
3 ordsets:intersection          3.44 M      290.38 ns  ±9494.06%     0 ns     1000 ns
0 cerl_sets:intersection        1.62 M      618.37 ns  ±5703.54%     0 ns     1000 ns
2 gb_sets:intersection          1.48 M      677.41 ns  ±4388.76%  1000 ns     1000 ns

Comparison:
1 mapsets:intersection          4.61 M
3 ordsets:intersection          3.44 M - 1.34x slower +73.54 ns
0 cerl_sets:intersection        1.62 M - 2.85x slower +401.53 ns
2 gb_sets:intersection          1.48 M - 3.12x slower +460.57 ns

##### With input d2 Equal (10) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          3.96 M      252.22 ns ±10397.76%     0 ns     1000 ns
3 ordsets:intersection          2.95 M      338.84 ns  ±8900.72%     0 ns     1000 ns
0 cerl_sets:intersection        1.16 M      862.62 ns  ±3981.08%  1000 ns     1000 ns
2 gb_sets:intersection          0.90 M     1112.16 ns  ±2553.42%  1000 ns     2000 ns

Comparison:
1 mapsets:intersection          3.96 M
3 ordsets:intersection          2.95 M - 1.34x slower +86.61 ns
0 cerl_sets:intersection        1.16 M - 3.42x slower +610.40 ns
2 gb_sets:intersection          0.90 M - 4.41x slower +859.94 ns

##### With input d3 Equal (30) #####
Name                               ips        average  deviation   median      99th %
1 mapsets:intersection          2.31 M        0.43 μs  ±8998.97%     0 μs        1 μs
3 ordsets:intersection          1.49 M        0.67 μs  ±3628.66%     1 μs        1 μs
0 cerl_sets:intersection        0.52 M        1.94 μs   ±965.82%     2 μs        3 μs
2 gb_sets:intersection          0.42 M        2.38 μs   ±878.07%     2 μs        4 μs

Comparison:
1 mapsets:intersection          2.31 M
3 ordsets:intersection          1.49 M - 1.55x slower +0.24 μs
0 cerl_sets:intersection        0.52 M - 4.48x slower +1.51 μs
2 gb_sets:intersection          0.42 M - 5.50x slower +1.95 μs

元组整数集合的并集 #

Operating System: macOS
CPU Information: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Number of Available Cores: 8
Available memory: 16 GB
Elixir 1.9.0
Erlang 23-master

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
Estimated total run time: 4.90 min

##### With input a1 Interspersed (5) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        2.53 M      394.70 ns  ±7692.39%     0 ns       1000 ns
3 ordsets:intersection        2.12 M      471.60 ns  ±1021.75%     0 ns       1000 ns
2 gb_sets:intersection        1.30 M      768.44 ns  ±2657.04%  1000 ns       1000 ns

Comparison:
1 mapsets:intersection        2.53 M
3 ordsets:intersection        2.12 M - 1.19x slower +76.90 ns
2 gb_sets:intersection        1.30 M - 1.95x slower +373.75 ns

##### With input a2 Interspersed (10) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        1.96 M      510.95 ns  ±2509.15%     0 ns       1000 ns
3 ordsets:intersection        1.30 M      770.06 ns   ±676.65%  1000 ns       1000 ns
2 gb_sets:intersection        0.81 M     1240.22 ns  ±1388.14%  1000 ns       2000 ns

Comparison:
1 mapsets:intersection        1.96 M
3 ordsets:intersection        1.30 M - 1.51x slower +259.11 ns
2 gb_sets:intersection        0.81 M - 2.43x slower +729.27 ns

##### With input a3 Interspersed (30) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection      845.89 K        1.18 μs  ±2713.20%     1 μs          2 μs
3 ordsets:intersection      495.26 K        2.02 μs   ±164.49%     2 μs          3 μs
2 gb_sets:intersection      324.61 K        3.08 μs   ±718.13%     3 μs          5 μs

Comparison:
1 mapsets:intersection      845.89 K
3 ordsets:intersection      495.26 K - 1.71x slower +0.84 μs
2 gb_sets:intersection      324.61 K - 2.61x slower +1.90 μs

##### With input b1 Half-left (5) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        4.66 M      214.57 ns  ±1896.59%     0 ns       1000 ns
3 ordsets:intersection        3.62 M      276.50 ns  ±1465.48%     0 ns       1000 ns
2 gb_sets:intersection        1.73 M      577.07 ns  ±5041.95%     0 ns       1000 ns

Comparison:
1 mapsets:intersection        4.66 M
3 ordsets:intersection        3.62 M - 1.29x slower +61.94 ns
2 gb_sets:intersection        1.73 M - 2.69x slower +362.51 ns

##### With input b2 Half-left (10) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        2.92 M      342.24 ns  ±9961.99%     0 ns       1000 ns
3 ordsets:intersection        2.09 M      478.76 ns  ±5507.02%     0 ns       1000 ns
2 gb_sets:intersection        0.96 M     1043.40 ns  ±2396.75%  1000 ns       2000 ns

Comparison:
1 mapsets:intersection        2.92 M
3 ordsets:intersection        2.09 M - 1.40x slower +136.53 ns
2 gb_sets:intersection        0.96 M - 3.05x slower +701.17 ns

##### With input b3 Half-left (30) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        1.72 M      580.48 ns  ±4998.64%     0 ns       1000 ns
3 ordsets:intersection        1.01 M      989.96 ns  ±2850.03%  1000 ns       2000 ns
2 gb_sets:intersection        0.44 M     2292.44 ns   ±981.37%  2000 ns       4000 ns

Comparison:
1 mapsets:intersection        1.72 M
3 ordsets:intersection        1.01 M - 1.71x slower +409.48 ns
2 gb_sets:intersection        0.44 M - 3.95x slower +1711.96 ns

##### With input b4 Half-left (50) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection      902.32 K        1.11 μs  ±1892.28%     1 μs          2 μs
3 ordsets:intersection      710.61 K        1.41 μs  ±1793.08%     1 μs          2 μs
2 gb_sets:intersection      282.62 K        3.54 μs   ±495.73%     3 μs         11 μs

Comparison:
1 mapsets:intersection      902.32 K
3 ordsets:intersection      710.61 K - 1.27x slower +0.30 μs
2 gb_sets:intersection      282.62 K - 3.19x slower +2.43 μs

##### With input c1 Halt-right (5) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        4.70 M      212.66 ns  ±1573.58%     0 ns       1000 ns
3 ordsets:intersection        3.77 M      265.19 ns  ±1597.40%     0 ns       1000 ns
2 gb_sets:intersection        1.76 M      567.11 ns  ±4249.42%     0 ns       1000 ns

Comparison:
1 mapsets:intersection        4.70 M
3 ordsets:intersection        3.77 M - 1.25x slower +52.53 ns
2 gb_sets:intersection        1.76 M - 2.67x slower +354.45 ns

##### With input c2 Halt-right (10) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        3.14 M      318.35 ns  ±7626.82%     0 ns       1000 ns
3 ordsets:intersection        2.23 M      449.20 ns  ±5268.98%     0 ns       1000 ns
2 gb_sets:intersection        0.99 M     1014.32 ns  ±2177.84%  1000 ns       2000 ns

Comparison:
1 mapsets:intersection        3.14 M
3 ordsets:intersection        2.23 M - 1.41x slower +130.85 ns
2 gb_sets:intersection        0.99 M - 3.19x slower +695.97 ns

##### With input c3 Halt-right (30) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        1.78 M      560.38 ns  ±5118.91%     0 ns       1000 ns
3 ordsets:intersection        1.01 M      989.13 ns  ±2292.17%  1000 ns       2000 ns
2 gb_sets:intersection        0.44 M     2294.68 ns   ±981.21%  2000 ns       4000 ns

Comparison:
1 mapsets:intersection        1.78 M
3 ordsets:intersection        1.01 M - 1.77x slower +428.75 ns
2 gb_sets:intersection        0.44 M - 4.09x slower +1734.30 ns

##### With input c4 Half-right (50) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection      875.40 K        1.14 μs  ±1770.92%     1 μs          2 μs
3 ordsets:intersection      703.96 K        1.42 μs  ±1911.40%     1 μs          3 μs
2 gb_sets:intersection      294.25 K        3.40 μs   ±488.43%     3 μs          6 μs

Comparison:
1 mapsets:intersection      875.40 K
3 ordsets:intersection      703.96 K - 1.24x slower +0.28 μs
2 gb_sets:intersection      294.25 K - 2.98x slower +2.26 μs

##### With input d1 Equal (5) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        3.29 M      303.69 ns  ±9348.28%     0 ns       1000 ns
3 ordsets:intersection        2.19 M      455.98 ns  ±5799.97%     0 ns       1000 ns
2 gb_sets:intersection        1.15 M      869.11 ns  ±3884.46%  1000 ns       2000 ns

Comparison:
1 mapsets:intersection        3.29 M
3 ordsets:intersection        2.19 M - 1.50x slower +152.29 ns
2 gb_sets:intersection        1.15 M - 2.86x slower +565.41 ns

##### With input d2 Equal (10) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection        2.93 M      341.11 ns  ±3839.65%     0 ns       1000 ns
3 ordsets:intersection        1.85 M      540.08 ns  ±2436.90%     0 ns       1000 ns
2 gb_sets:intersection        0.72 M     1388.21 ns  ±1540.59%  1000 ns       2000 ns

Comparison:
1 mapsets:intersection        2.93 M
3 ordsets:intersection        1.85 M - 1.58x slower +198.97 ns
2 gb_sets:intersection        0.72 M - 4.07x slower +1047.11 ns

##### With input d3 Equal (30) #####
Name                             ips        average  deviation   median        99th %
1 mapsets:intersection     1395.63 K        0.72 μs  ±4359.84%     1 μs          1 μs
3 ordsets:intersection      744.64 K        1.34 μs  ±1845.56%     1 μs          2 μs
2 gb_sets:intersection      302.52 K        3.31 μs   ±672.80%     3 μs         10 μs

Comparison:
1 mapsets:intersection     1395.63 K
3 ordsets:intersection      744.64 K - 1.87x slower +0.63 μs
2 gb_sets:intersection      302.52 K - 4.61x slower +2.59 μs