Separate Chaining Hash Table

A C++17 std::unordered_map/std::unordered_set compatible replacement that can be tuned for memory efficiency or/and speed.

The hash table uses separate chaining for collision resolution. The hash table maintains several buckets for storing elements. In case that the hash table is initialized as a hash map, a bucket consists of a key and a value array, called key_bucket and value_bucket. For the hash set case, there is no value_bucket.

Motivation

In this hash table, a bucket storing keys and values uses to separate arrays, i.e., an array for the keys and an array for the values. This layout makes it possbile to store keys and values more efficiently in case that they are plain integers with a bit width smaller than the word size (< 64 bits). First, a std::pair<key,value> is not stored byte-packed, using memory that is a multiple of the word size. Second, finding a key in a large key_bucket is faster than in a bucket storing std::pair<key,value> elements, since more keys can fit into the cache line.

Usage

The library is header-only and can be included with #include <separate_chaining_map.hpp>.

The hash table is called separate_chaining_table. There are two typedefs separate_chaining_map and separate_chaining_set for creating a unordered_map or unordered_set, respectively. The template parameters are:

• key_bucket_t<storage_t> the type of bucket to store keys of type storage_t. These are defined in bucket.hpp, and are

  • class_bucket for the most general case
  • plain_bucket for the case that the keys can be copied with std::memcpy (complicated classes with copy constructors must be maintained in a class_bucket)
  • avx2_bucket for the case that the keys are integers and that the CPU supports the AVX2 instruction set.
  • varwidth_bucket for the case that the keys are integers and that there is an arbitrary maximum bit width of the integers to store. This is beneficient in combination with a compact hash function (see below). However, operations on this bucket take more time.

• value_bucket_t the type of bucket to store values. Possible classes are class_bucket and plain_bucket, which can also store values instead of keys. Like in the description above, use class_bucket for non-std::memcpy-able value types.

• hash_mapping_t is a mapping that takes a key and returns, based on the number of the buckets of the hash table, a pair consisting of a hash-value and a remainder.

  • The hash value is an integer in [0, bucket_count()-1].
  • The remainder is defined such that the keys can be restored from the pair. In the most simple case, the remainder is the key. This fact is used by the class hash_mapping_adapter<storage_t, hash_function> that turns a standard hash function hash_funtion hashing storage_t elements into a hash_mapping_t. Since the hash table can restore a key by having its hash value v and its remainder r, it stores r in the v-th bucket instead of the key. A non-trivial mapping is xorshift_hash<storage_t, key_t>. Here, the bit width of the remainder of type storage_t is the bit width of the key of type key_t minus log2(bucket_count()). In conjunction with varwidth_bucket, this fact can be used to represent the keys in less bits than their bit width. This technique is also called quotienting. Another way is to allocate sufficiently large memory to store keys of a specific bit width in a plain_bucket or avx2_bucket storing remainders with a smaller bit width. For instance, 24-bit keys can be stored in plain_bucket<uint8_t> if there are 2^{24} / 2^{8} = 2^16 = 65536 buckets.

• resize_strategy_t defines what to do when inserting an element in a full bucket.

  • incremental_resize lets a bucket grow incrementally, which means that a bucket is always full, and that each insertion results in a malloc call. On the bright side, each bucket takes exactly as much memory as needed. Moreover, there is no need to store the capacities of the buckets.
    and that there is no space wasted.
  • arbitrary_resize increases the size of a bucket in relation to its current size. The current implementation doubles the size s of a bucket until s is larger than a fixed threshold. After surpassing the threshold, the size is increased merely by 50% (inspired by the discussion of Folly's vector). This behavior can be adjusted in arbitrary_resize::resize.

Compact Chaining Map

The map compact_chaining_map is the most space efficient but also most time consuming hash table layout storing keys and values that are integers. It combines the key and the value bucket in a single bucket (and thus using only one pointer instead of two). The bucket is first filled with the keys, and then subsequently with the values. It can also store values of arbitrary bit widths (not necessarily quantisized by eight).

Global Constants

You can specify the following macros to overwrite the behavior of the hash table:

• SEPARATE_MAX_BUCKET_SIZE : Changes the number of maximum elements a bucket can store. Use a value between 1 and 255.

Key Splitting

Given the bit widths of the keys has an interesting distribution, it is also possible to combine several hash tables with an adapter, such that each hash table is responsible for keys whose bit width are within a given range. This adapter allows each hash table to adjust the needed space for the quotient. The class keysplit_adapter<map_type, max_bits, m_length> is a hash map adapter for storing keys up to bit width max_bits. Therefore, it uses an array of map_type hash maps. This array has length m_length. The range [0...max_bits] is equi-distantly distributed to the hash maps of this array. However, since xorshift_hash does not work with integers having a bit width of 64, there is also a class keysplit_adapter64<map_type, large_map_type, m_length> that wraps around keysplit_adapter<map_type, 63, m_length>. This class uses the map large_map_type for storing keys with bit width 64.

Bucket Table

For small data sets (< 100 elements), it is faster and more memory efficient to use a single bucket without hashing by relying on large caches during the linear scanning process. The class bucket_table wraps a single bucket in a map/set interface.

Usage

• Elements can be searched with find
• The map can be used with the handy []-operator for retrieving and writing values.
• find_or_insert can be used to insert a key with a default value, or retrieve this key's value if it has already been inserted.
• the hash table is serializable with standard streams std::istream and std::ostream. When storing many keys of a small domain with varwidth_bucket, one can likely achieve a compression by serializing the hash table instead of storing the elements in their plain form.

Implementation Details and Advanced Usage

• A bucket stores initially INITIAL_BUCKETS many buckets. This constant is defined for each resize_strategy_t differently. For arbitrary_resize, this size can be arbitrarily chosen.
• A bucket can grow up to MAX_BUCKET_BYTESIZE elements. This value is linked with the type bucketsize_type representing integers up to MAX_BUCKET_BYTESIZE.
• erase does not free memory. For that, use fit_to_shrink.
• The typedefs for hash map and hash sets wrap the value bucket type value_bucket_t around a manager for the array of value buckets, which is either realized by value_array_manager using the straight-forward way (for emulating a hash map), or value_dummy_manager for storing no value at all (for emulating a hash set).
• Since a bucket is split into a key and a value array, there is no natural std::pair representation of an element. This means that an iterator has to create a pair on the fly, which can cause a slowdown. Instead, you can use the navigator interface with the methods key() and value().
• If you want to process and delete processed elements like you would do with a stack or queue, start at rbegin_nav and end at rend_nav, using decremental operation on the navigator object.
• The internal_type of varwidth_bucket can be changed to a different integer type. If interal_type has x bits, then the data is stored in an array of elements using x bits, i.e., the space is quantisized by x. Small integers can save space will large integers give a speed-up due to fewer malloc calls.

Caveats

• You cannot use an avx2_bucket with overloaded malloc/free.
• There is no specizalization for serialization of a custom hash function. For instance, you obtain a corrupted hash table on deserialization when using a hash function that dynamically generates seeds.

Dependencies

• Command line tools
  • cmake
  • make
  • a C++17 compiler like gcc or clang
  • gtest (optional) for tests

Compilation

git submodule init
git submodule update
mkdir -p build
cd build
cmake ..
make
./example_map

There is also a Dockerfile available that runs the above commands on an environment having g++ and cmake installed.

Outlook

It is possible to extend this approach for Cuckoo Hashing with multiple hash functions.

Related Work

• DySECT: uses Cuckoo hashing with cache-optimized buckets. Our approach has orthogonal features (AXV2 / quotienting) that can be combined with this hash table layout.
• tsl::sparse_map: sparse hash tables using quadratic probing
• bonsai tables: A set of hash tables using compact hashing and linear probing for collision resolution. The linear probing makes it difficult to maintain a remainder with hash value v at position v in the hash table. For that additional maintaince is required that needs extra space and slows down the computation. On the other hand, it does not need buckets, and therefore can maintain elements more efficiently if the space requirement is known in advance.