[eeps] EEP ???: Maps based set implementation
Anthony Ramine
n.oxyde@REDACTED
Fri Sep 20 16:57:37 CEST 2019
FYI that EEP is not properly transmitted as UTF-8 and José's name becomes mojibake. Would be nice if people on your side would fix that.
> Le 20 sept. 2019 à 15:59, Raimo Niskanen <raimo+eeps@REDACTED> a écrit :
>
> The EEP has been added to the EEP repository as EEP 50.
>
> http://erlang.org/eep/eeps/eep-0050.html
>
> Unfortunately I do not know the trick to update
> https://www.erlang.org/erlang-enhancement-proposals/eep-0000.html
>
> / Raimo Niskanen, EEP Editor
>
>
>
> On Wed, Sep 18, 2019 at 05:22:06PM +0200, José Valim wrote:
>> Author: José Valim <jose(dot)valim(at)gmail(dot)com>
>> Status: Draft
>> Type: Standards Track
>> Created: 18-Sep-2019
>> Post-History:
>> ****
>> EEP ???: Maps based set implementation
>> ----
>>
>> Abstract
>> ========
>>
>> This EEP proposes a maps-based set implementation and a group of BIFs
>> with the goal of providing a *de facto* sets implementation in Erlang/OTP.
>>
>> Motivation
>> ==========
>>
>> In order to efficiently use sets in Erlang/OTP today, one has to
>> consider three different options:
>>
>> * `ordsets`
>> * `gb_sets`
>> * using maps as sets (such as `cerl_sets`)
>>
>> For example, if you wish to perform unions/intersections/subtractions,
>> `ordsets` is generally the most efficient. For individual lookups,
>> `gb_sets` and "maps as sets" are preferred, although the latter has no
>> official API in Erlang/OTP. If you need a mixed profile, the best choice
>> becomes blurrier. Note there is also a `sets` module, but it is rarely a
>> viable option.
>>
>> The current landscape with sets is not much different than the dictionary
>> landscape before Erlang/OTP 17. Luckily, once `maps` were added, `maps`
>> became the *de facto* dictionary in Erlang. The other dictionary-like
>> modules
>> may perform better under limited occasions but `maps` provide the best
>> profile in many scenarios and are a reasonable starting point (until a
>> need for benchmarking and profiling arises - if it ever arises).
>>
>> The goal of this EEP is to propose a map-based sets solution with a group
>> of BIFs that will give developers a sets implementation that can be
>> generally
>> treated as the main set implementation in Erlang/OTP.
>>
>> Rationale
>> =========
>>
>> Dictionaries and sets implementation tend to walk side-by-side. Such as
>> `ordsets` and `orddict`, `gb_trees` and `gb_sets`. That's because you can
>> consider elements in a set to be keys in a dictionary, where you don't care
>> about the value for the keys.
>>
>> Given we have dictionaries implemented as maps, could we have sets based
>> on maps? The answer is yes and there are two approaches. The first approach
>> is to provide a native data structure, implemented in C, with its own
>> syntax.
>> The advantage of said approach would be lower memory usage, but it has a
>> large
>> impact on the language and on the runtime. Therefore that's not the approach
>> we will pursue here.
>>
>> The second approach, which this EEP advocates for, is to implement `sets`
>> on top of maps, as done by `cerl_sets`. In this scenario, the sets elements
>> are keys in the map and the values are empty lists (we chose empty lists
>> because they are very cheap to serialize).
>>
>> Using "maps as sets" provide good performance characteristics today for
>> inserting, adding and deleting set elements, being faster than all other
>> implementations. However, in terms of memory usage, "maps as sets" use
>> almost two times more memory than `ordsets` (although note that the set
>> operations themselves may end-up using less memory). Compared to `gb_sets`,
>> "maps as sets" use less memory altogether.
>>
>> But can "maps as sets" be as fast as `ordsets` for unions, intersections and
>> subtractions?
>>
>> The good news is: **this is already true for unions**, which is equivalent
>> to
>> `maps:merge/2`. Benchmarks are available in the addendum and we can take the
>> following conclusions:
>>
>> 1. when unioning integers elements, maps and ordsets take roughly the same
>> time, with maps slightly ahead except in cases where we have to go from
>> small maps to large maps
>>
>> 2. when unioning tuples elements, maps are consistently faster, sometimes
>> 2 to 4 times, except in cases where we have to go from small maps to
>> large
>> maps. This is expected, the more expensive it becomes to compare items,
>> the more expensive `ordsets` become
>>
>> This means that, if we could implement intersection and subtraction on top
>> of
>> maps, then it will likely be more efficient than ordsets, since intersection
>> and subtraction do not have the issue of map resizing.
>>
>> A proof of concept was written for intersections using small and mixed maps
>> with positive results (see benchmarks in addendum). We can also see the new
>> intersections are consistently faster than `cerl_sets`. Unfortunately there
>> are no benchmarks for intersections between two large maps due to lack of C
>> expertise of this EEP author. The assumption, which should be verified, is
>> that intersecting large maps will be faster than intersecting large
>> `ordsets`.
>> Given the results seen in `maps:merge/2` and the fact that map resizing does
>> not happen on intersections, this assumption will likely turn out to be
>> true.
>>
>> Therefore, if our goal is to make `maps` as fast as `ordsets` for those
>> operations, we need to implement new BIFs.
>>
>> Specification
>> =============
>>
>> "maps as sets" are generally more efficient than the existing set
>> implementations for checking, adding and deleting elements. However,
>> they are slower than `ordsets` in the following operations:
>>
>> * `from_list/1`
>> * `is_subset/2`
>> * `is_disjoint/2`
>> * `intersection/2`
>> * `subtract/2`
>>
>> Therefore, if we want to have a *de facto* set implementation, the functions
>> above would have to implemented as BIFs. The first three provide only
>> partial
>> speed-ups compared to a pure Erlang implementation but the last two
>> operations
>> with provide drastic gains as NIFs. The last two operations are also the
>> most
>> complex to implement.
>>
>> With the changes above, the only operations in "maps as sets" that won't be
>> as
>> fast or faster than "ordsets" is `to_list` and `fold`, since `ordsets` are
>> lists
>> internally.
>>
>> Assuming the functionality above is validated as more performant (at least
>> for intersections and subtractions) and there is an interest in providing
>> said
>> functionality, the last question is: how should this functionality be
>> exposed?
>>
>> Possible APIs for "maps as sets"
>> ================================
>>
>> ### 1. Augment the maps module
>>
>> If there is no interest in adding new module to OTP, the "maps" module could
>> be augmented to have set-based operations. In those cases, only the keys are
>> compared. The values can come from either the first or the second map.
>>
>> While this approach will improve performance, the `intersection/2` and
>> `subtract/2`
>> APIs in `maps` are quite awkward. One alternative is to prefix those
>> operations
>> with the `key` prefix, such as `keyintersection`, to make it clear they are
>> about the intersection of keys. But perhaps a better approach altogether is
>> to define a separate module.
>>
>> ### 2. Add `mapsets` module
>>
>> The `mapsets` module provide sets based on maps. The fact said sets are
>> based
>> on maps is part of the public API (i.e. they are not an opaque type),
>> exactly
>> like `ordsets`. The value for each key is the empty list to make sure sets
>> can
>> be cheapily serialized.
>>
>> This new module would have 5 BIFs:
>>
>> * `mapsets:from_list/1`
>> * `mapsets:intersection/2`
>> * `mapsets:is_subset/2`
>> * `mapsets:is_disjoint/2`
>> * `mapsets:subtract/2`
>>
>> The remaining APIs would be implemented on top of the maps API.
>>
>> ### 3. Change the `sets` module
>>
>> Another option, similar to the above, is to leverage the fact the `sets`
>> type
>> is opaque and replace its implementation by "maps as sets". The advantagess
>> of
>> this approach is that everyone using `sets` today would get a performance
>> upgrade
>> and we would avoid adding a new module to Erlang/OTP. After all, there is
>> always
>> a risk that by adding a fourth option that unifies all three existing
>> options,
>> we will simply end-up with four options.
>>
>> The downside of this approach is that, although the `sets` datastructure is
>> opaque, developers may have serialized it elsewhere, and therefore the
>> existing
>> data structure must still be supported. This means we would first need to
>> modify
>> the `sets` module to support both old sets and the new "maps as sets".
>> Support
>> for the old data structure can be removed only in future versions. We would
>> also
>> need to discuss an appropriate migration path.
>>
>> Next Steps
>> ==========
>>
>> At the current stage, the proposal is a draft and not fully specified. In
>> particular, it is necessary to validate the implementation of some
>> operations
>> and benchmark them. It is also necessary to choose a relevant API for the
>> propose functionality.
>>
>> That said, if this proposal is viewed positively, the proposed next steps
>> are:
>>
>> 1. Validate that intersections with maps is faster than with ordsets
>>
>> 2. Choose the desired API for "maps as sets" (i.e. choose between 1.
>> extending
>> `maps`, 2. adding `mapsets`, or 3. changing `sets`)
>>
>> 3. Implement the chosen API in Erlang (most of the `cerl_sets`
>> implementation
>> can be leveraged)
>>
>> 4. Optimize the relevant operations as BIFs
>>
>> The author of the EEP can help by implementating step 3.
>>
>> Copyright
>> =========
>>
>> This document has been placed in the public domain.
>>
>> [EmacsVar]: <> "Local Variables:"
>> [EmacsVar]: <> "mode: indented-text"
>> [EmacsVar]: <> "indent-tabs-mode: nil"
>> [EmacsVar]: <> "sentence-end-double-space: t"
>> [EmacsVar]: <> "fill-column: 70"
>> [EmacsVar]: <> "coding: utf-8"
>> [EmacsVar]: <> "End:"
>> [VimVar]: <> " vim: set fileencoding=utf-8 expandtab shiftwidth=4
>> softtabstop=4: "
>>
>>
>> Addendum: Union benchmark results
>> =================================
>>
>> ### Unioning sets of integers
>>
>> 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
>>
>> ### Unioning sets of tuple-integers
>>
>> 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
>>
>> Addendum: Intersection benchmark results
>> ========================================
>>
>> ### Intersection of sets of integers
>>
>> 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
>>
>> ### Unioning sets of tuple-integers
>>
>> 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
>
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>> http://erlang.org/mailman/listinfo/eeps
>
>
> --
>
> / Raimo Niskanen, Erlang/OTP, Ericsson AB
> _______________________________________________
> eeps mailing list
> eeps@REDACTED
> http://erlang.org/mailman/listinfo/eeps
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