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Update documentation for new FCA implementation
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@@ -1,5 +1,6 @@
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[#buckets]
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:idprefix: buckets_
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:imagesdir: ../diagrams
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= The Data Structure
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@@ -8,7 +9,7 @@ any number of elements. For example, the following diagram shows an <<unordered_
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`B`, `C`, `D` and `E` (this is just for illustration, containers will typically
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have more buckets).
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image::../diagrams/buckets.png[]
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image::buckets.png[]
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In order to decide which bucket to place an element in, the container applies
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the hash function, `Hash`, to the element's key (for `unordered_set` and
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@@ -150,3 +151,334 @@ x.rehash(std::ceil(n / x.max_load_factor()))
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+
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See the <<unordered_map_rehash,reference for more details>> on the `rehash` function.
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== Fast Closed Addressing Implementation
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++++
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<style>
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.imageblock > .title {
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text-align: inherit;
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}
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</style>
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++++
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Boost.Unordered sports one of the fastest implementations of closed addressing, also commonly known as https://en.wikipedia.org/wiki/Hash_table#Separate_chaining[separate chaining]. An example figure representing the data structure is below:
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[#img-bucket-groups,.text-center]
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.A simple bucket group approach
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image::bucket-groups.png[align=center]
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An array of "buckets" is allocated and each bucket in turn points to its own individual linked list. This makes meeting the standard requirements of bucket iteration straight-forward. Unfortunately, iteration of the entire container is often times slow using this layout as each bucket must be examined for occupancy, yielding a time complexity of `O(bucket_count() + size())` when the standard requires complexity to be `O(size())`.
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Canonical standard implementations will wind up looking like the diagram below:
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[.text-center]
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.The canonical standard approach
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image::singly-linked.png[align=center,link=../diagrams/singly-linked.png,window=_blank]
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It's worth noting that this approach is only used by pass:[libc++] and pass:[libstdc++]; the MSVC Dinkumware implementation uses a different one. A more detailed analysis of the standard containers can be found http://bannalia.blogspot.com/2013/10/implementation-of-c-unordered.html[here].
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This unusually laid out data structure is chosen to make iteration of the entire container efficient by inter-connecting all of the nodes into a singly-linked list. One might also notice that buckets point to the node _before_ the start of the bucket's elements. This is done so that removing elements from the list can be done efficiently without introducing the need for a doubly-linked list. Unfortunately, this data structure introduces a guaranteed extra indirection. For example, to access the first element of a bucket, something like this must be done:
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```c++
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auto const idx = get_bucket_idx(hash_function(key));
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node* p = buckets[idx]; // first load
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node* n = p->next; // second load
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if (n && is_in_bucket(n, idx)) {
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value_type const& v = *n; // third load
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// ...
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}
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```
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With a simple bucket group layout, this is all that must be done:
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```c++
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auto const idx = get_bucket_idx(hash_function(key));
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node* n = buckets[idx]; // first load
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if (n) {
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value_type const& v = *n; // second load
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// ...
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}
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```
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In practice, the extra indirection can have a dramatic performance impact to common operations such as `insert`, `find` and `erase`. But to keep iteration of the container fast, Boost.Unordered introduces a novel data structure, a "bucket group". A bucket group is a fixed-width view of a subsection of the buckets array. It contains a bitmask (a `std::size_t`) which it uses to track occupancy of buckets and contains two pointers so that it can form a doubly-linked list with non-empty groups. An example diagram is below:
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[#img-fca-layout]
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.The new layout used by Boost
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image::fca.png[align=center]
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Thus container-wide iteration is turned into traversing the non-empty bucket groups (an operation with constant time complexity) which reduces the time complexity back to `O(size())`. In total, a bucket group is only 4 words in size and it views `sizeof(std::size_t) * CHAR_BIT` buckets meaning that for all common implementations, there's only 4 bits of space overhead per bucket introduced by the bucket groups.
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For more information on implementation rationale, read the <<Implementation Rationale, corresponding section>>.
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= Benchmarks
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All benchmarks were created using `unordered_set<unsigned int>` (non-duplicate) and `unordered_multiset<unsigned int>` (duplicate). The source code can be https://github.com/joaquintides/boost_unordered_benchmark[found here].
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The insertion benchmarks insert `n` random values, where `n` is between 10,000 and 3 million. For the duplicated benchmarks, the same random values are repeated an average of 5 times.
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The erasure benchmarks erase all `n` elements randomly until the container is empty.
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The successful lookup benchmarks are done by looking up all `n` values, in the their original insertion order.
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The unsuccessful lookup benchmarks use `n` randomly generated integers but using a different seed value.
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== GCC 11 + libstdc++-v3
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=== Insertion
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/gcc/running insertion.xlsx.practice.png[width=250,link=../diagrams/benchmarks/gcc/running insertion.xlsx.practice.png,window=_blank]
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|image::benchmarks/gcc/running%20insertion.xlsx.practice non-unique.png[width=250,link=../diagrams/benchmarks/gcc/running%20insertion.xlsx.practice non-unique.png,window=_blank]
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|image::benchmarks/gcc/running%20insertion.xlsx.practice non-unique 5.png[width=250,link=../diagrams/benchmarks/gcc/running%20insertion.xlsx.practice non-unique 5.png,window=_blank]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements +
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max load factor 5
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|===
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/gcc/running%20insertion.xlsx.practice norehash.png[width=250,link=../diagrams/benchmarks/gcc/running%20insertion.xlsx.practice norehash.png,window=_blank]
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|image::benchmarks/gcc/running%20insertion.xlsx.practice norehash non-unique.png[width=250,link=../diagrams/benchmarks/gcc/running%20insertion.xlsx.practice norehash non-unique.png,window=_blank]
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|image::benchmarks/gcc/running%20insertion.xlsx.practice norehash non-unique 5.png[width=250,link=../diagrams/benchmarks/gcc/running%20insertion.xlsx.practice norehash non-unique 5.png,window=_blank]
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h|non-duplicate elements, +
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prior `reserve`
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h|duplicate elements, +
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prior `reserve`
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h|duplicate elements, +
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max load factor 5, +
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prior `reserve`
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|===
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=== Erasure
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/gcc/scattered%20erasure.xlsx.practice.png[width=250,link=../diagrams/benchmarks/gcc/scattered%20erasure.xlsx.practice.png,window=_blank]
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|image::benchmarks/gcc/scattered%20erasure.xlsx.practice non-unique.png[width=250,link=../diagrams/benchmarks/gcc/scattered%20erasure.xlsx.practice non-unique.png,window=_blank]
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|image::benchmarks/gcc/scattered%20erasure.xlsx.practice non-unique 5.png[width=250,link=../diagrams/benchmarks/gcc/scattered%20erasure.xlsx.practice non-unique 5.png,window=_blank]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements +
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max load factor 5
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|===
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=== Successful Lookup
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice.png]
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|image::benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice non-unique.png]
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|image::benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
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max load factor 5
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|===
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=== Unsuccessful lookup
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice.png]
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|image::benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice non-unique.png]
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|image::benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
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max load factor 5
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|===
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== Clang 12 + libc++
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=== Insertion
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/clang_libcpp/running%20insertion.xlsx.practice.png[width=250, window=_blank,link=../diagrams/benchmarks/clang_libcpp/running%20insertion.xlsx.practice.png]
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|image::benchmarks/clang_libcpp/running%20insertion.xlsx.practice non-unique.png[width=250, window=_blank,link=../diagrams/benchmarks/clang_libcpp/running%20insertion.xlsx.practice non-unique.png]
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|image::benchmarks/clang_libcpp/running%20insertion.xlsx.practice non-unique 5.png[width=250, window=_blank,link=../diagrams/benchmarks/clang_libcpp/running%20insertion.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
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max load factor 5
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|===
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/clang_libcpp/running%20insertion.xlsx.practice norehash.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/running%20insertion.xlsx.practice norehash.png]
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|image::benchmarks/clang_libcpp/running%20insertion.xlsx.practice norehash non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/running%20insertion.xlsx.practice norehash non-unique.png]
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|image::benchmarks/clang_libcpp/running%20insertion.xlsx.practice norehash non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/running%20insertion.xlsx.practice norehash non-unique 5.png]
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h|non-duplicate elements, +
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prior `reserve`
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h|duplicate elements, +
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prior `reserve`
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h|duplicate elements, +
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max load factor 5, +
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prior `reserve`
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|===
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=== Erasure
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice.png]
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|image::benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice non-unique.png]
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|image::benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
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max load factor 5
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|===
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=== Successful lookup
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/clang_libcpp/scattered%20successful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20successful%20looukp.xlsx.practice.png]
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|image::benchmarks/clang_libcpp/scattered%20successful%20looukp.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20successful%20looukp.xlsx.practice non-unique.png]
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|image::benchmarks/clang_libcpp/scattered%20successful%20looukp.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20successful%20looukp.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
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max load factor 5
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|===
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=== Unsuccessful lookup
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/clang_libcpp/scattered%20unsuccessful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20unsuccessful%20looukp.xlsx.practice.png]
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|image::benchmarks/clang_libcpp/scattered%20unsuccessful%20looukp.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20unsuccessful%20looukp.xlsx.practice non-unique.png]
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|image::benchmarks/clang_libcpp/scattered%20unsuccessful%20looukp.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20unsuccessful%20looukp.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
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max load factor 5
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|===
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== Visual Studio 2019 + Dinkumware
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=== Insertion
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/vs/running%20insertion.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice.png]
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|image::benchmarks/vs/running%20insertion.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice non-unique.png]
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|image::benchmarks/vs/running%20insertion.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
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max load factor 5
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|===
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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|===
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|image::benchmarks/vs/running%20insertion.xlsx.practice norehash.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice norehash.png]
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|image::benchmarks/vs/running%20insertion.xlsx.practice norehash non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice norehash non-unique.png]
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|image::benchmarks/vs/running%20insertion.xlsx.practice norehash non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice norehash non-unique 5.png]
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|
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h|non-duplicate elements, +
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prior `reserve`
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h|duplicate elements, +
|
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prior `reserve`
|
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h|duplicate elements, +
|
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max load factor 5, +
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prior `reserve`
|
||||
|
||||
|===
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||||
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=== Erasure
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||||
|
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[caption=]
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[cols="3*^.^a", frame=all, grid=all]
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||||
|===
|
||||
|
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|image::benchmarks/vs/scattered%20erasure.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20erasure.xlsx.practice.png]
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|image::benchmarks/vs/scattered%20erasure.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20erasure.xlsx.practice non-unique.png]
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|image::benchmarks/vs/scattered%20erasure.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20erasure.xlsx.practice non-unique 5.png]
|
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|
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h|non-duplicate elements
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h|duplicate elements
|
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h|duplicate elements, +
|
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max load factor 5
|
||||
|
||||
|===
|
||||
|
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=== Successful lookup
|
||||
|
||||
[caption=]
|
||||
[cols="3*^.^a", frame=all, grid=all]
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||||
|===
|
||||
|
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|image::benchmarks/vs/scattered%20successful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/benchmarks/vs/scattered%20successful%20looukp.xlsx.practice.png]
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|image::benchmarks/vs/scattered%20successful%20looukp.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/benchmarks/vs/scattered%20successful%20looukp.xlsx.practice non-unique.png]
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|image::benchmarks/vs/scattered%20successful%20looukp.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/benchmarks/vs/scattered%20successful%20looukp.xlsx.practice non-unique 5.png]
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|
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h|non-duplicate elements
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h|duplicate elements
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h|duplicate elements, +
|
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max load factor 5
|
||||
|
||||
|===
|
||||
|
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=== Unsuccessful lookup
|
||||
|
||||
[caption=]
|
||||
[cols="3*^.^a", frame=all, grid=all]
|
||||
|===
|
||||
|
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|image::benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice.png]
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|image::benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice non-unique.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice non-unique.png]
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|image::benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice non-unique 5.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice non-unique 5.png]
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h|non-duplicate elements
|
||||
h|duplicate elements
|
||||
h|duplicate elements, +
|
||||
max load factor 5
|
||||
|
||||
|===
|
||||
Reference in new issue
Block a user