Update documentation for new FCA implementation

This commit is contained in:
Christian Mazakas
2022-06-01 11:45:56 -07:00
parent 110c5dcf10
commit 18503e5eb8
52 changed files with 531 additions and 1 deletions

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doc/roadmap.md Normal file
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@ -0,0 +1,188 @@
# Refactoring Roadmap
[Proof of concept](https://github.com/joaquintides/fca_unordered) implementation for a fast closed-addressing implementation.
## Plan of Refactoring
* remove `ptr_node` and `ptr_bucket`
* see if the code can survive a lack of the `extra_node` or maybe we hard-code it in
* implement bucket groups as they are in `fca` but don't use them directly yet, add alongside the `buckets_` data member in `struct table`
* try to remove `bucket_info_` from the node structure (breaks all call-sites that use `get_bucket()` and dependents)
* make sure `fca` can successfully handle multi-variants at this stage + supports mutable iterators for `map`/`multimap`
* do a hard-break:
* update code to no longer use one single linked list across all buckets (each bucket contains its own unique list)
* integrate the `bucket_group<Node>` structure into the `table` (update iterator call-sites to include `bucket_iterator`s)
Blockers:
* how to handle `multi` variants with new `fca` prototype
## Implementation Differences
### Unordered
### Node Type
Bullet Points:
* reify node type into a single one
* come up with implementation for multi- variants
* code that touches `get_bucket()` and `*_in_group()` member functions may need updating
There are two node types in Unordered, `struct node` and `struct ptr_node`, and the node type is selected conditionally based on the Allocator's pointer type:
```c++
template <typename A, typename T, typename NodePtr, typename BucketPtr>
struct pick_node2
{
typedef boost::unordered::detail::node<A, T> node;
// ...
};
template <typename A, typename T>
struct pick_node2<A, T, boost::unordered::detail::ptr_node<T>*,
boost::unordered::detail::ptr_bucket*>
{
typedef boost::unordered::detail::ptr_node<T> node;
// ...
};
template <typename A, typename T> struct pick_node
{
typedef typename boost::remove_const<T>::type nonconst;
typedef boost::unordered::detail::allocator_traits<
typename boost::unordered::detail::rebind_wrap<A,
boost::unordered::detail::ptr_node<nonconst> >::type>
tentative_node_traits;
typedef boost::unordered::detail::allocator_traits<
typename boost::unordered::detail::rebind_wrap<A,
boost::unordered::detail::ptr_bucket>::type>
tentative_bucket_traits;
typedef pick_node2<A, nonconst, typename tentative_node_traits::pointer,
typename tentative_bucket_traits::pointer>
pick;
typedef typename pick::node node;
typedef typename pick::bucket bucket;
typedef typename pick::link_pointer link_pointer;
};
```
The node types are identical in terms of interface and the only difference is that `node` is chosen when the Allocator uses fancy pointers and `ptr_node` is chosen when the Allocator's pointer type is `T*`.
Nodes in Unorderd store `bucket_info_`:
```cpp
template <typename A, typename T>
struct node : boost::unordered::detail::value_base<T>
{
link_pointer next_;
std::size_t bucket_info_;
node() : next_(), bucket_info_(0) {}
// ...
};
```
`bucket_info_` maps each node back to its corresponding bucket via the member function:
```cpp
std::size_t get_bucket() const
{
return bucket_info_ & ((std::size_t)-1 >> 1);
}
```
`bucket_info_` is also used to demarcate the start of equivalent nodes in the containers via:
```cpp
// Note that nodes start out as the first in their group, as `bucket_info_` defaults to 0.
std::size_t is_first_in_group() const
{ return !(bucket_info_ & ~((std::size_t)-1 >> 1)); }
void set_first_in_group()
{ bucket_info_ = bucket_info_ & ((std::size_t)-1 >> 1); }
void reset_first_in_group()
{ bucket_info_ = bucket_info_ | ~((std::size_t)-1 >> 1); }
```
A goal of refactoring is to simply have one node type:
```cpp
template<class T>
struct node {
node *next;
T value;
};
```
that is used unconditionally. This also requires updating the code that touches the `bucket_info_` along with the code that that touches the `*_in_group()` member functions.
### Bucket Type
Bullet points:
* reify bucket structure into a single one
* figure out how to add `bucket_group`s to the table struct
Buckets are similar to nodes in that there are two variations: `template<class NodePointer> struct bucket` and `struct ptr_bucket`.
The buckets exist to contain a pointer to a node, however they contain an `enum { extra_node = true };` or `enum { extra_node = false }` to determine whether or not the code should explicitly allocate a default constructed node whose address assigned as the dummy node at the end of the bucket array.
`extra_node` is used in the creation and deletion of the bucket array but it is not inherently clear what its intended purpose is.
### Iterators
Iterators are currently templated on the type of Node they store. Because `fca` constructs iterators with two arguments, all the call-sites that instantiate iterators will need to be updated but this a straight-forward mechanical change.
Iterators are selected, as of now, via the `detail::map` and `detail::set` class templates.
For example, for `unordered_map`, `iterator` is defined as:
```cpp
typedef boost::unordered::detail::map<A, K, T, H, P> types;
typedef typename types::table table;
typedef typename table::iterator iterator;
```
The iterator is a member typedef of the `table` which is `types::table`. Examining `types` (aka `detail::map<...>`), we see:
```cpp
template <typename A, typename K, typename M, typename H, typename P>
struct map {
// ...
typedef boost::unordered::detail::table<types> table;
// ...
};
```
Examining the `detail::table<types>` struct, we see:
```cpp
template <typename Types>
struct table {
// ...
typedef typename Types::iterator iterator;
// ...
}
```
Collapsing all of this, we see that our iterator types are defined here:
```cpp
template <typename A, typename K, typename M, typename H, typename P>
struct map
{
// ...
typedef boost::unordered::detail::pick_node<A, value_type> pick;
typedef typename pick::node node;
typedef boost::unordered::iterator_detail::iterator<node> iterator;
typedef boost::unordered::iterator_detail::c_iterator<node> c_iterator;
typedef boost::unordered::iterator_detail::l_iterator<node> l_iterator;
typedef boost::unordered::iterator_detail::cl_iterator<node>
cl_iterator;
// ...
};
```
This is similarly designed for `detail::set`:
```cpp
typedef boost::unordered::iterator_detail::c_iterator<node> iterator;
typedef boost::unordered::iterator_detail::c_iterator<node> c_iterator;
typedef boost::unordered::iterator_detail::cl_iterator<node> l_iterator;
typedef boost::unordered::iterator_detail::cl_iterator<node>
cl_iterator;
```
The only difference here is that `set::iterator` is always a `c_iterator`, a `const_iterator` type.

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@ -1,5 +1,6 @@
[#buckets]
:idprefix: buckets_
:imagesdir: ../diagrams
= The Data Structure
@ -8,7 +9,7 @@ any number of elements. For example, the following diagram shows an <<unordered_
`B`, `C`, `D` and `E` (this is just for illustration, containers will typically
have more buckets).
image::../diagrams/buckets.png[]
image::buckets.png[]
In order to decide which bucket to place an element in, the container applies
the hash function, `Hash`, to the element's key (for `unordered_set` and
@ -150,3 +151,334 @@ x.rehash(std::ceil(n / x.max_load_factor()))
+
See the <<unordered_map_rehash,reference for more details>> on the `rehash` function.
== Fast Closed Addressing Implementation
++++
<style>
.imageblock > .title {
text-align: inherit;
}
</style>
++++
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:
[#img-bucket-groups,.text-center]
.A simple bucket group approach
image::bucket-groups.png[align=center]
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())`.
Canonical standard implementations will wind up looking like the diagram below:
[.text-center]
.The canonical standard approach
image::singly-linked.png[align=center,link=../diagrams/singly-linked.png,window=_blank]
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].
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:
```c++
auto const idx = get_bucket_idx(hash_function(key));
node* p = buckets[idx]; // first load
node* n = p->next; // second load
if (n && is_in_bucket(n, idx)) {
value_type const& v = *n; // third load
// ...
}
```
With a simple bucket group layout, this is all that must be done:
```c++
auto const idx = get_bucket_idx(hash_function(key));
node* n = buckets[idx]; // first load
if (n) {
value_type const& v = *n; // second load
// ...
}
```
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:
[#img-fca-layout]
.The new layout used by Boost
image::fca.png[align=center]
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.
For more information on implementation rationale, read the <<Implementation Rationale, corresponding section>>.
= Benchmarks
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].
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.
The erasure benchmarks erase all `n` elements randomly until the container is empty.
The successful lookup benchmarks are done by looking up all `n` values, in the their original insertion order.
The unsuccessful lookup benchmarks use `n` randomly generated integers but using a different seed value.
== GCC 11 + libstdc++-v3
=== Insertion
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/gcc/running insertion.xlsx.practice.png[width=250,link=../diagrams/benchmarks/gcc/running insertion.xlsx.practice.png,window=_blank]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements +
max load factor 5
|===
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/gcc/running%20insertion.xlsx.practice norehash.png[width=250,link=../diagrams/benchmarks/gcc/running%20insertion.xlsx.practice norehash.png,window=_blank]
|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]
|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]
h|non-duplicate elements, +
prior `reserve`
h|duplicate elements, +
prior `reserve`
h|duplicate elements, +
max load factor 5, +
prior `reserve`
|===
=== Erasure
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/gcc/scattered%20erasure.xlsx.practice.png[width=250,link=../diagrams/benchmarks/gcc/scattered%20erasure.xlsx.practice.png,window=_blank]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements +
max load factor 5
|===
=== Successful Lookup
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20successful%20looukp.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
=== Unsuccessful lookup
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/gcc/scattered%20unsuccessful%20looukp.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
== Clang 12 + libc++
=== Insertion
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/clang_libcpp/running%20insertion.xlsx.practice.png[width=250, window=_blank,link=../diagrams/benchmarks/clang_libcpp/running%20insertion.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|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]
|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]
|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]
h|non-duplicate elements, +
prior `reserve`
h|duplicate elements, +
prior `reserve`
h|duplicate elements, +
max load factor 5, +
prior `reserve`
|===
=== Erasure
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/clang_libcpp/scattered%20erasure.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
=== Successful lookup
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|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]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
=== Unsuccessful lookup
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|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]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
== Visual Studio 2019 + Dinkumware
=== Insertion
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/vs/running%20insertion.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/vs/running%20insertion.xlsx.practice norehash.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/running%20insertion.xlsx.practice norehash.png]
|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]
|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]
h|non-duplicate elements, +
prior `reserve`
h|duplicate elements, +
prior `reserve`
h|duplicate elements, +
max load factor 5, +
prior `reserve`
|===
=== Erasure
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/vs/scattered%20erasure.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20erasure.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
=== Successful lookup
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/vs/scattered%20successful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/benchmarks/vs/scattered%20successful%20looukp.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===
=== Unsuccessful lookup
[caption=]
[cols="3*^.^a", frame=all, grid=all]
|===
|image::benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice.png[width=250,window=_blank,link=../diagrams/benchmarks/vs/scattered%20unsuccessful%20looukp.xlsx.practice.png]
|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]
|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]
h|non-duplicate elements
h|duplicate elements
h|duplicate elements, +
max load factor 5
|===

View File

@ -6,6 +6,12 @@
:github-pr-url: https://github.com/boostorg/unordered/pull
:cpp: C++
== Release 1.80.0
* Refactor internal implementation to be dramatically faster
* Fix long-standing bug where `final`-qualified Hasher and KeyEqual couldn't be
used
== Release 1.79.0
* Improved {cpp}20 support:

View File

@ -66,3 +66,7 @@ by using `(h * m) >> (w - k)`, where `h` is the hash value, `m` is the golden
ratio multiplied by `2^w`, `w` is the word size (32 or 64), and `2^k` is the
number of buckets. This provides a good compromise between speed and
distribution.
Since release 1.80.0, prime numbers are chosen for the number of buckets in
tandem with sophisticated modulo arithmetic. This removes the need for "mixing"
the result of the user's hash function as was used for release 1.79.0.