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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<html>
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<head>
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<title>Hash-Based Containers</title>
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<meta name="GENERATOR" content="Microsoft Visual Studio .NET 7.1">
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<meta name="vs_targetSchema" content="http://schemas.microsoft.com/intellisense/ie5">
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</head>
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<body bgcolor = "white">
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<h1>Hash-Based Containers</h1>
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<p>
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This section describes hash-based containers. It is organized
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as follows.
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</p>
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<ol>
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<li>
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<a href = "#overview">Overview</a> is an overview.
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</li>
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<li>
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<a href = "#hash_policies">Hash Policies</a> discusses
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hash policies.
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</li>
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<li>
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<a href = "#resize_policies">Resize Policies</a> discusses
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resize policies.
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</li>
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<li>
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<a href = "#policy_interaction">Policy Interaction</a> discusses
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interaction between policies.
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</li>
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</ol>
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<h2><a name = "overview">Overview</a></h2>
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<p>
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Figure
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<a href = "#hash_cd">Hash-based containers</a>
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shows the container-hierarchy; the hash-based containers are circled.
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<a href = "cc_hash_assoc_cntnr.html"><tt>cc_hash_assoc_cntnr</tt></a>
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is a collision-chaining hash-based container;
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<a href = "gp_hash_assoc_cntnr.html"><tt>gp_hash_assoc_cntnr</tt></a>
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is a (general) probing hash-based container.
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</p>
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<h6 align = "center">
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<a name = "hash_cd">
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<img src = "hash_cd.jpg" width = "70%" alt = "no image">
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</h6>
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<h6 align = "center">
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</a>
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Hash-based containers.
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</h6>
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<p>
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The collision-chaining hash-based container has the following declaration.
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</p>
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<pre>
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<b>template</b><
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<b>typename</b> Key,
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<b>typename</b> Data,
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<b>class</b> Hash_Fn = std::hash<Key>,
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<b>class</b> Eq_Fn = std::equal_to<Key>,
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<b>class</b> Comb_Hash_Fn =
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<a href = "direct_mask_range_hashing.html">direct_mask_range_hashing</a><>
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<b>class</b> Resize_Policy = <i>default explained below.</i>
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<b>bool</b> Store_Hash = <b>false</b>,
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<b>class</b> Allocator =
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std::allocator<<b>char</b>> >
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<b>class</b> <a href = "cc_hash_assoc_cntnr.html">cc_hash_assoc_cntnr</a>;
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</pre>
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<p>
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The parameters have the following meaning:
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</p>
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<ol>
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<li> <tt>Key</tt> is the key type.
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</li>
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<li> <tt>Data</tt> is the data-policy, and is explained in
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<a href = "ms_gen.html#ds_policy">Mapping-Semantics Genericity::Data Types as a Policy</a>.
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</li>
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<li> <tt>Hash_Fn</tt> is a key hashing functor.</li>
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<li> <tt>Eq_Fn</tt> is a key equivalence functor.</li>
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<li> <tt>Comb_Hash_Fn</tt> is a <i>range-hashing_functor</i>; it
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describes how to translate hash values into positions within the table.
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This is described in
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<a name = "#hash_policies">Hash Policies</a>.</li>
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</li>
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<li> <tt>Resize_Policy</tt> describes how a container object should
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change its internal size. This is described in
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<a name = #resize_policies">Resize Policies</a>.</li>
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<li> <tt>Store_Hash</tt> indicates whether the hash value should
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be stored with each entry. This is described in
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<a name = "#policy_interaction">Policy Interaction</a>.</li>
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<li> <tt>Allocator</tt> is (surprisingly) an allocator type.
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</li>
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</ol>
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<p>
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The probing hash-based container has the following declaration.
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</p>
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<pre>
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<b>template</b><
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<b>typename</b> Key,
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<b>typename</b> Data,
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<b>class</b> Hash_Fn =
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std::hash<
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Key>,
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<b>class</b> Eq_Fn =
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std::equal_to<
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Key>,
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<b>class</b> Comb_Probe_Fn =
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<a href = "direct_mask_range_hashing.html">direct_mask_range_hashing</a><>
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<b>class</b> Probe_Fn = <i>default explained below.</i>
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<b>class</b> Resize_Policy = <i>default explained below.</i>
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<b>bool</b> Store_Hash = <b>false</b>,
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<b>class</b> Allocator =
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std::allocator<<b>char</b>> >
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<b>class</b> <a href = "gp_hash_assoc_cntnr.html">gp_hash_assoc_cntnr</a>;
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</pre>
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<p>
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The parameters are identical to those of the collision-chaining container, except
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for the following.
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</p>
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<ol>
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<li> <tt>Comb_Probe_Fn</tt> describes how to transform a probe sequence into
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a sequence of positions within the table.
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</li>
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<li> <tt>Probe_Fn</tt> describes a probe sequence policy.</li>
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</ol>
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<p>
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Some of the default template values depend on the values of other parameters,
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and are explained in
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<a name = "#policy_interaction">Policy Interaction</a>.
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</p>
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<h2><a name = "hash_policies">Hash Policies</h2></a>
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<p>
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This subsection describes hash policies. It is organized as follows:
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</p>
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<ol>
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<li> <a href = "#general_terms">General Terms</a> describes
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some general terms.
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</li>
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<li> <a href = "#range_hashing_fns">Range-Hashing Functions</a>
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describes range-hasing functions.</li>
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<li> <a href = "#hash_policies_ranged_hash_policies">Ranged-Hash Functions</a>
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describes ranged-hash functions. </li>
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<li> <a href = "#pb_assoc_imp">Implementation in <tt>pb_assoc</tt></a>
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describes the implementation of these concepts in <tt>pb_assoc</tt>.
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</li>
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</ol>
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<h3><a name="general_terms">General Terms</a></h3>
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<p>
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There
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are actually three functions involved in transforming a key into a hash-table's
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position (see Figure
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<a href = "#hash_ranged_hash_range_hashing_fns">
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Hash runctions, ranged-hash functions, and range-hashing functions
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</a>):
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</p>
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<ol>
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<li>
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A <i>ranged-hash</i> function, which maps keys into an interval of the
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non-negative integrals. This is the function actually required by the
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hash-table algorithm.
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</li>
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<li>
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A hash function, which maps keys into non-negative integral types. This is
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typically specified by the writer of the key class.
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</li>
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<li>
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A <i>range-hashing</i> function, which maps non-negative integral types into an
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interval of non-negative integral types.
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</li>
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</ol>
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<h6 align = "center">
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<a name = "hash_ranged_hash_range_hashing_fns">
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<img src = "hash_ranged_hash_range_hashing_fns.jpg" width = "70%" alt = "no image">
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</h6>
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<h6 align = "center">
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</a>
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Hash runctions, ranged-hash functions, and range-hashing functions.
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</h6>
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<p>
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Let <i>U</i> be a domain (<i>e.g.</i>, the integers, or the strings of 3
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characters). A hash-table algorithm needs to map elements of <i>U</i> "uniformly"
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into the range <i>[0,..., m - 1]</i> (where <i>m</i> is a non-negative integral
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value, and is, in general, time varying). <i>I.e.</i>, the algorithm needs a <i>ranged-hash</i>
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function
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</p>
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<p>
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<i>f : U × Z<sub>+</sub> → Z<sub>+</sub> </i>,
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</p>
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<p>
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such that for any <i>u</i> in <i>U</i>
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,
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</p>
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<p>
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<i>0 ≤ f(u, m) ≤ m - 1 </i>,
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</p>
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<p>
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and which has "good uniformity" properties [<a href="references.html#knuth98sorting">knuth98sorting</a>].
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One common solution is to use the composition of the hash function
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</p>
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<p>
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<i>h : U → Z<sub>+</sub> </i>,
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</p>
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<p>
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which maps elements of <i>U</i> into the non-negative integrals, and
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</p>
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<p>
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<i>g : Z<sub>+</sub> × Z<sub>+</sub> → Z<sub>+</sub>, </i>
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</p>
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<p>
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which maps a non-negative hash value, and a non-negative range upper-bound into
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a non-negative integral in the range between 0 (inclusive) and the range upper
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bound (exclusive), <i>i.e.</i>, for any <i>r</i> in <i>Z<sub>+</sub></i>,
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</p>
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<p>
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<i>0 ≤ g(r, m) ≤ m - 1 </i>.
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</p>
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<p>
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The resulting ranged-hash function, is
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</p>
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<p>
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<i><a name="eqn:ranged_hash_composed_of_hash_and_range_hashing">f(u , m) = g(h(u), m) </a>
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</i>(1) .
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</p>
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<p>
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From the above, it is obvious that given <i>g</i> and <i>h</i>, <i>f</i> can
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always be composed (however the converse is not true). The STL's hash-based
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containers allow specifying a hash function, and use a hard-wired range-hashing function; the ranged-hash function is implicitly composed.
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</p>
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<p>
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The above describes the case where a key is to be mapped into a <i>single
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position</i> within a hash table, <i>e.g.</i>, in a collision-chaining table.
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In other cases, a key is to be mapped into a <i>sequence of poisitions</i>
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within a table, <i>e.g.</i>, in a probing table.
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</p>
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<p>
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Similar terms apply in this case: the table requires a <i>ranged probe</i>
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function, mapping a key into a sequence of positions withing the table. This is
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typically acheived by composing a <i>hash function</i> mapping the key
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into a non-negative integral type, a <i>probe</i> function transforming the
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hash value into a sequence of hash values, and a <i>range-hashing</i> function
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transforming the sequence of hash values into a sequence of positions.
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</p>
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<h3><a name="range_hashing_fns">Range-Hashing Functions</a></h3>
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<p>
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Some common choices for range-hashing functions are the division,
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multiplication, and middle-square methods [<a href="references.html#knuth98sorting">knuth98sorting</a>],
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defined as
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</p>
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<p>
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<i><a name="eqn:division_method">g(r, m) = r mod m </a></i>(2) ,
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</p>
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<p>
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<i>g(r, m) = ⌈ u/v ( a r mod v ) ⌉ </i>,
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</p>
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<p>
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and
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</p>
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<p>
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<i>g(r, m) = ⌈ u/v ( r<sup>2</sup> mod v ) ⌉ </i>,
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</p>
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<p>
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respectively, for some positive integrals <i>u</i> and <i>v</i> (typically
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powers of 2), and some <i>a</i>. Each of these range-hashing functions works
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best for some different setting.
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</p>
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<p>
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The division method <a href="#division_method">(2)</a> is a very common
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choice. However, even this single method can be implemented in two very
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different ways. It is possible to implement <a href="#division_method">(2)</a>
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using the low level <i>%</i> (modulo) operation (for any <i>m</i>), or the low
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level <i>&</i> (bit-mask) operation (for the case where <i>m</i> is a power of
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2), <i>i.e.</i>,
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</p>
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<p>
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<i><a name="eqn:division_method_prime_mod">g(r, m) = r % m </a></i>(3) ,
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</p>
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<p>
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and
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</p>
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<p>
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<a name="eqn:division_method_bit_mask">
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<i>g(r, m) = r & m - 1, ( m = 2<sup>k</sup>
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</i>
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for some<i> k) </i></a>(4) ,
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</p>
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<p>
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respectively.
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</p>
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<p>
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The <i>%</i> (modulo) implementation <a href="#division_method_prime_mod">(3)</a>
|
| 316 |
|
|
has the advantage that for <i>m</i> a prime far from a power of 2, <i>g(r, m)</i>
|
| 317 |
|
|
is affected by all the bits of <i>r</i> (minimizing the chance of collision).
|
| 318 |
|
|
It has the disadvantage of using the costly modulo operation. This method is
|
| 319 |
|
|
hard-wired into SGI's implementation [<a href="references.html#sgi_stl">sgi_stl</a>].
|
| 320 |
|
|
</p>
|
| 321 |
|
|
|
| 322 |
|
|
<p>
|
| 323 |
|
|
The <i>&</i> (bit-mask) implementation <a href="#division_method_bit_mask">(4)</a>
|
| 324 |
|
|
has the advantage of relying on the fast bitwise and operation. It has the
|
| 325 |
|
|
disadvantage that for <i>g(r, m)</i> is affected only by the low order bits of <i>r</i>.
|
| 326 |
|
|
This method is hard-wired into Dinkumware's implementation [<a href="references.html#dinkumware_stl">dinkumware_stl</a>].
|
| 327 |
|
|
</p>
|
| 328 |
|
|
|
| 329 |
|
|
|
| 330 |
|
|
|
| 331 |
|
|
|
| 332 |
|
|
<h3><a name="hash_policies_ranged_hash_policies">Ranged-Hash Functions</a></h3>
|
| 333 |
|
|
|
| 334 |
|
|
<p>
|
| 335 |
|
|
In some less frequent cases it is beneficial to allow the client to
|
| 336 |
|
|
directly specify a ranged-hash hash function. It is true, that the writer of
|
| 337 |
|
|
the ranged-hash function cannot rely on the values of <i>m</i> having specific
|
| 338 |
|
|
numerical properties suitable for hashing (in the sense used in [<a href="references.html#knuth98sorting">knuth98sorting</a>]),
|
| 339 |
|
|
since the values of <i>m</i> are determined by a resize policy with possibly
|
| 340 |
|
|
orthogonal considerations.
|
| 341 |
|
|
</p>
|
| 342 |
|
|
|
| 343 |
|
|
<p>
|
| 344 |
|
|
There are two cases where a ranged-hash function can be superior. The firs is when using perfect hashing
|
| 345 |
|
|
[<a href="references.html#knuth98sorting">knuth98sorting</a>]; the second
|
| 346 |
|
|
is when the values of <i>m</i> can be used to estimate the
|
| 347 |
|
|
"general" number of distinct values required. This is described in the following.
|
| 348 |
|
|
</p>
|
| 349 |
|
|
|
| 350 |
|
|
<p>
|
| 351 |
|
|
Let
|
| 352 |
|
|
</p>
|
| 353 |
|
|
|
| 354 |
|
|
<p>
|
| 355 |
|
|
<i>s = [ s<sub>0</sub>,..., s<sub>t - 1</sub>] </i>
|
| 356 |
|
|
</p>
|
| 357 |
|
|
|
| 358 |
|
|
<p>
|
| 359 |
|
|
be a string of <i>t</i> characters, each of which is from domain <i>S</i>.
|
| 360 |
|
|
Consider the following ranged-hash function:
|
| 361 |
|
|
</p>
|
| 362 |
|
|
|
| 363 |
|
|
<p>
|
| 364 |
|
|
<a name="eqn:total_string_dna_hash">
|
| 365 |
|
|
<i>
|
| 366 |
|
|
f<sub>1</sub>(s, m) =
|
| 367 |
|
|
∑ <sub>i =
|
| 368 |
|
|
0</sub><sup>t - 1</sup> s<sub>i</sub> a<sup>i</sup> </i>mod<i> m </i>
|
| 369 |
|
|
</a> (5) ,
|
| 370 |
|
|
</p>
|
| 371 |
|
|
|
| 372 |
|
|
<p>
|
| 373 |
|
|
where <i>a</i> is some non-negative integral value. This is the standard
|
| 374 |
|
|
string-hashing function used in SGI's implementation (with <i>a = 5</i>) [<a href="references.html#sgi_stl">sgi_stl</a>].
|
| 375 |
|
|
Its advantage is that it takes into account all of the characters of the
|
| 376 |
|
|
string.
|
| 377 |
|
|
</p>
|
| 378 |
|
|
|
| 379 |
|
|
<p>
|
| 380 |
|
|
Now assume that <i>s</i> is the string representation of a of a long DNA
|
| 381 |
|
|
sequence (and so <i>S = {'A', 'C', 'G', 'T'}</i>). In this case, scanning the
|
| 382 |
|
|
entire string might be prohibitively expensive. A possible alternative might be
|
| 383 |
|
|
to use only the first <i>k</i> characters of the string, where
|
| 384 |
|
|
</p>
|
| 385 |
|
|
|
| 386 |
|
|
<p>
|
| 387 |
|
|
k <sup>|S|</sup> ≥ m ,
|
| 388 |
|
|
</p>
|
| 389 |
|
|
<p>
|
| 390 |
|
|
<i>i.e.</i>, using the hash function
|
| 391 |
|
|
</p>
|
| 392 |
|
|
<p>
|
| 393 |
|
|
<a name="eqn:only_k_string_dna_hash"><i>f<sub>2</sub>(s, m) = ∑ <sub>i = 0</sub><sup>k
|
| 394 |
|
|
- 1</sup> s<sub>i</sub> a<sup>i</sup> </i>mod <i>m </i></a>, (6)
|
| 395 |
|
|
</p>
|
| 396 |
|
|
<p>
|
| 397 |
|
|
requiring scanning over only
|
| 398 |
|
|
</p>
|
| 399 |
|
|
<p>
|
| 400 |
|
|
<i>k = </i>log<i><sub>4</sub>( m ) </i>
|
| 401 |
|
|
</p>
|
| 402 |
|
|
<p>
|
| 403 |
|
|
characters.
|
| 404 |
|
|
</p>
|
| 405 |
|
|
<p>
|
| 406 |
|
|
Other more elaborate hash-functions might scan <i>k</i> characters starting at
|
| 407 |
|
|
a random position (determined at each resize), or scanning <i>k</i> random
|
| 408 |
|
|
positions (determined at each resize), <i>i.e.</i>, using
|
| 409 |
|
|
</p>
|
| 410 |
|
|
<p>
|
| 411 |
|
|
<i>f<sub>3</sub>(s, m) = ∑ <sub>i = r<sub>0</sub></sub><sup>r<sub>0</sub> + k - 1</sup>
|
| 412 |
|
|
s<sub>i</sub> a<sup>i</sup> </i>mod <i>m </i>,
|
| 413 |
|
|
</p>
|
| 414 |
|
|
<p>
|
| 415 |
|
|
or
|
| 416 |
|
|
</p>
|
| 417 |
|
|
<p>
|
| 418 |
|
|
<i>f<sub>4</sub>(s, m) = ∑ <sub>i = 0</sub><sup>k - 1</sup> s<sub>r<sub>i</sub></sub>
|
| 419 |
|
|
a<sup>r<sub>i</sub></sup> </i>mod <i>m </i>,
|
| 420 |
|
|
</p>
|
| 421 |
|
|
<p>
|
| 422 |
|
|
<p>
|
| 423 |
|
|
respectively, for <i>r<sub>0</sub>,..., r<sub>k-1</sub></i> each in the
|
| 424 |
|
|
(inclusive) range <i>[0,...,t-1]</i>.
|
| 425 |
|
|
</p>
|
| 426 |
|
|
|
| 427 |
|
|
|
| 428 |
|
|
<h3><a name="pb_assoc_imp">Implementation in <tt>pb_assoc</tt></a></h3>
|
| 429 |
|
|
|
| 430 |
|
|
<p>
|
| 431 |
|
|
<a href = "cc_hash_assoc_cntnr.html"><tt>cc_hash_assoc_cntnr</tt></a> is
|
| 432 |
|
|
parameterized by <tt>Hash_Fn</tt> and <tt>Comb_Hash_Fn</tt>, a hash functor
|
| 433 |
|
|
and a combining hash functor, respectively.
|
| 434 |
|
|
</p>
|
| 435 |
|
|
|
| 436 |
|
|
<p>
|
| 437 |
|
|
For any hash functor except <a href = "null_hash_fn.html"><tt>null_hash_fn</tt></a>,
|
| 438 |
|
|
one of the
|
| 439 |
|
|
<a href = "concepts.html#concepts_null_policies">Concepts::Null Policy Classes</a>,
|
| 440 |
|
|
then <tt>Comb_Hash_Fn</tt> is considered a range-hashing functor.
|
| 441 |
|
|
The container will synthesize a ranged-hash functor from both. For example, Figure
|
| 442 |
|
|
<a href = "#hash_range_hashing_seq_diagram">
|
| 443 |
|
|
Insert hash sequence diagram
|
| 444 |
|
|
</a>
|
| 445 |
|
|
shows an <tt>insert</tt> sequence diagram. The user inserts an element (point A),
|
| 446 |
|
|
the container transforms the key into a non-negative integral using the hash
|
| 447 |
|
|
functor (points B and C), and transforms the result into a position
|
| 448 |
|
|
using the combining functor (points D and E).
|
| 449 |
|
|
</p>
|
| 450 |
|
|
|
| 451 |
|
|
<h6 align = "center">
|
| 452 |
|
|
<a name = "hash_range_hashing_seq_diagram">
|
| 453 |
|
|
<img src = "hash_range_hashing_seq_diagram.jpg" width = "70%" alt = "no image">
|
| 454 |
|
|
</a>
|
| 455 |
|
|
</h6>
|
| 456 |
|
|
<h6 align = "center">
|
| 457 |
|
|
Insert hash sequence diagram.
|
| 458 |
|
|
</h6>
|
| 459 |
|
|
|
| 460 |
|
|
|
| 461 |
|
|
<p>
|
| 462 |
|
|
<tt>pb_assoc</tt> contains the following range-hashing policies:
|
| 463 |
|
|
</p>
|
| 464 |
|
|
|
| 465 |
|
|
<ol>
|
| 466 |
|
|
<li>
|
| 467 |
|
|
<a href = "direct_mask_range_hashing.html"><tt>direct_mask_range_hashing</tt></a>
|
| 468 |
|
|
and
|
| 469 |
|
|
<a href = "direct_mod_range_hashing.html"><tt>direct_mod_range_hashing</tt></a>
|
| 470 |
|
|
are range-hashing functions based on a bit-mask and a modulo operation, respectively.
|
| 471 |
|
|
</li>
|
| 472 |
|
|
</ol>
|
| 473 |
|
|
|
| 474 |
|
|
|
| 475 |
|
|
<p>
|
| 476 |
|
|
If <tt>Comb_Hash_Fn</tt> is instantiated by
|
| 477 |
|
|
<a href = "null_hash_fn.html"><tt>null_hash_fn</tt></a>,
|
| 478 |
|
|
and a combining-hash functor, the container treats
|
| 479 |
|
|
the combining hash functor as a ranged-hash function. For example, Figure
|
| 480 |
|
|
<a href = "#hash_range_hashing_seq_diagram2">
|
| 481 |
|
|
Insert hash sequence diagram with a null combination policy
|
| 482 |
|
|
</a>
|
| 483 |
|
|
shows an <tt>insert</tt> sequence diagram. The user inserts an element (point A),
|
| 484 |
|
|
the container transforms the key into a position
|
| 485 |
|
|
using the combining functor (points B and C).
|
| 486 |
|
|
</p>
|
| 487 |
|
|
|
| 488 |
|
|
|
| 489 |
|
|
<h6 align = "center">
|
| 490 |
|
|
<a name = "hash_range_hashing_seq_diagram2">
|
| 491 |
|
|
<img src = "hash_range_hashing_seq_diagram2.jpg" width = "70%" alt = "no image">
|
| 492 |
|
|
</a>
|
| 493 |
|
|
</h6>
|
| 494 |
|
|
<h6 align = "center">
|
| 495 |
|
|
Insert hash sequence diagram with a null combination policy.
|
| 496 |
|
|
</h6>
|
| 497 |
|
|
|
| 498 |
|
|
<p>
|
| 499 |
|
|
Similarly,
|
| 500 |
|
|
<a href = "gp_hash_assoc_cntnr.html"></a><tt>gp_hash_assoc_cntnr</tt>
|
| 501 |
|
|
is parameterized by <tt>Hash_Fn</tt>, <tt>Probe_Fn</tt>, and
|
| 502 |
|
|
<tt>Comb_Probe_Fn</tt>. As before, if <tt>Probe_Fn</tt>
|
| 503 |
|
|
and <tt>Comb_Probe_Fn</tt> are, respectively,
|
| 504 |
|
|
<a href = "null_hash_fn.html"><tt>null_hash_fn</tt></a> and
|
| 505 |
|
|
<a href = "null_probe_fn.html"><tt>null_probe_fn</tt></a>,
|
| 506 |
|
|
then <tt>Comb_Probe_Fn</tt> is a ranged-probe functor. Otherwise, <tt>Hash_Fn</tt>
|
| 507 |
|
|
is a hash functor, <tt>Probe_Fn</tt> is a functor for offsets from a hash value,
|
| 508 |
|
|
and <tt>Comb_Probe_Fn</tt> transforms a probe sequence into a sequence of positions
|
| 509 |
|
|
within the table.
|
| 510 |
|
|
</p>
|
| 511 |
|
|
|
| 512 |
|
|
<p>
|
| 513 |
|
|
<tt>pb_assoc</tt> contains the following probe policies:
|
| 514 |
|
|
</p>
|
| 515 |
|
|
|
| 516 |
|
|
<ol>
|
| 517 |
|
|
<li>
|
| 518 |
|
|
<a href = "linear_probe_fn.html"><tt>linear_probe_fn</tt></a> is a linear probe
|
| 519 |
|
|
function.
|
| 520 |
|
|
</li>
|
| 521 |
|
|
<li>
|
| 522 |
|
|
<a href = "quadratic_probe_fn.html"><tt>quadratic_probe_fn</tt></a> is
|
| 523 |
|
|
a quadratic probe function.
|
| 524 |
|
|
</li>
|
| 525 |
|
|
</ol>
|
| 526 |
|
|
|
| 527 |
|
|
|
| 528 |
|
|
|
| 529 |
|
|
|
| 530 |
|
|
|
| 531 |
|
|
|
| 532 |
|
|
|
| 533 |
|
|
|
| 534 |
|
|
|
| 535 |
|
|
<h2><a name = "resize_policies">Resize Policies</a></h2>
|
| 536 |
|
|
|
| 537 |
|
|
<p>
|
| 538 |
|
|
This subsection describes resize policies. It is organized as follows:
|
| 539 |
|
|
</p>
|
| 540 |
|
|
|
| 541 |
|
|
<ol>
|
| 542 |
|
|
<li> <a href = "#general">General Terms</a> describes general
|
| 543 |
|
|
terms.
|
| 544 |
|
|
</li>
|
| 545 |
|
|
<li> <a href = "#size_policies">Size Policies</a> describes size
|
| 546 |
|
|
policies.
|
| 547 |
|
|
</li>
|
| 548 |
|
|
<li> <a href = "#trigger_policies">Trigger Policies</a> describes trigger
|
| 549 |
|
|
policies.
|
| 550 |
|
|
</li> <li> <a href = "#imp_pb_assoc">Implementation in <tt>pb_assoc</tt></a>
|
| 551 |
|
|
describes the implementation of these concepts in <tt>pb_assoc</tt>.
|
| 552 |
|
|
</li>
|
| 553 |
|
|
</ol>
|
| 554 |
|
|
|
| 555 |
|
|
|
| 556 |
|
|
<h3><a name = "general">General Terms</a></h3>
|
| 557 |
|
|
|
| 558 |
|
|
<p>
|
| 559 |
|
|
Hash-tables, as opposed to trees, do not naturally grow or shrink. It
|
| 560 |
|
|
is necessary to specify policies to determine how and when a hash table should change
|
| 561 |
|
|
its size.
|
| 562 |
|
|
</p>
|
| 563 |
|
|
|
| 564 |
|
|
<p>
|
| 565 |
|
|
In general, resize policies can be decomposed into (probably orthogonal)
|
| 566 |
|
|
policies:
|
| 567 |
|
|
</p>
|
| 568 |
|
|
<ol>
|
| 569 |
|
|
<li> A <i>size policy</i> indicating <i>how</i> a hash table should
|
| 570 |
|
|
grow (<i>e.g.,</i> it should multiply by powers of 2).
|
| 571 |
|
|
</li>
|
| 572 |
|
|
<li> A <i>trigger policy</i> indicating <i>when</i> a hash table should
|
| 573 |
|
|
grow (<i>e.g.,</i> a load factor is exceeded).
|
| 574 |
|
|
</li>
|
| 575 |
|
|
</ol>
|
| 576 |
|
|
|
| 577 |
|
|
|
| 578 |
|
|
|
| 579 |
|
|
<h3><a name = "size_policies">Size Policies</a></h3>
|
| 580 |
|
|
|
| 581 |
|
|
<p>
|
| 582 |
|
|
Size policies determine how a hash table
|
| 583 |
|
|
changes size. These policies are simple, and there are relatively
|
| 584 |
|
|
few sensible options. An exponential-size policy (with the initial
|
| 585 |
|
|
size and growth factors both powers of 2) works well with a
|
| 586 |
|
|
mask-based range-hashing function (see the <a href = "hash_policies.html#hash_policies_range_hashing_policies">Range-Hashing Policies</a> subsection),
|
| 587 |
|
|
and is the
|
| 588 |
|
|
hard-wired policy used by Dinkumware
|
| 589 |
|
|
[<a href = "references.html#dinkumware_stl">dinkumware_stl</a>]. A
|
| 590 |
|
|
prime-list based policy works well with a modulo-prime range
|
| 591 |
|
|
hashing function (see the <a href = "hash_policies.html#hash_policies_range_hashing_policies">Range-Hashing Policies</a> subsection),
|
| 592 |
|
|
and is the
|
| 593 |
|
|
hard-wired policy used by SGI's implementation
|
| 594 |
|
|
[<a href = "references.html#sgi_stl">sgi_stl</a>].
|
| 595 |
|
|
</p>
|
| 596 |
|
|
|
| 597 |
|
|
|
| 598 |
|
|
|
| 599 |
|
|
|
| 600 |
|
|
<h3><a name = "trigger_policies">Trigger Policies</a></h3>
|
| 601 |
|
|
|
| 602 |
|
|
<p>
|
| 603 |
|
|
Trigger policies determine when a hash table changes size.
|
| 604 |
|
|
Following is a description of two polcies: <i>load-check</i>
|
| 605 |
|
|
policies, and a collision-check policies.
|
| 606 |
|
|
</p>
|
| 607 |
|
|
|
| 608 |
|
|
<p>
|
| 609 |
|
|
Load-check policies are straightforward. The user
|
| 610 |
|
|
specifies two factors, <i>α<sub>min</sub></i> and <i>α<sub>max</sub></i>, and
|
| 611 |
|
|
the hash table maintains the invariant that
|
| 612 |
|
|
</p>
|
| 613 |
|
|
<p>
|
| 614 |
|
|
<i>
|
| 615 |
|
|
<a name = "eqn:load_factor_min_max">
|
| 616 |
|
|
α<sub>min</sub>
|
| 617 |
|
|
≤
|
| 618 |
|
|
(number of stored elements) / (hash-table size)
|
| 619 |
|
|
≤
|
| 620 |
|
|
α<sub>max</sub>
|
| 621 |
|
|
</a>
|
| 622 |
|
|
</i>
|
| 623 |
|
|
(1)
|
| 624 |
|
|
.
|
| 625 |
|
|
</p>
|
| 626 |
|
|
|
| 627 |
|
|
<p>
|
| 628 |
|
|
Collision-check policies work in the opposite direction of
|
| 629 |
|
|
load-check policies. They focus on keeping the number of
|
| 630 |
|
|
collisions moderate and hoping
|
| 631 |
|
|
that the size of the table will not grow very large,
|
| 632 |
|
|
instead of keeping a moderate load-factor and
|
| 633 |
|
|
hoping that the number of collisions will be small.
|
| 634 |
|
|
A
|
| 635 |
|
|
maximal collision-check policy resizes when the shortest
|
| 636 |
|
|
probe-sequence grows too large.
|
| 637 |
|
|
</p>
|
| 638 |
|
|
|
| 639 |
|
|
|
| 640 |
|
|
<p>
|
| 641 |
|
|
Consider Figure
|
| 642 |
|
|
<a href = "#balls_and_bins">Balls and bins</a>.
|
| 643 |
|
|
Let the size of the hash table be denoted by <i>m</i>, the
|
| 644 |
|
|
length of a probe sequence be denoted by <i>k</i>, and some load
|
| 645 |
|
|
factor be denoted by α. We would like to calculate the
|
| 646 |
|
|
minimal length of <i>k</i>, such that if there were <i>α m</i> elements
|
| 647 |
|
|
in the hash table, a probe sequence of length <i>k</i> would be found
|
| 648 |
|
|
with probability at most <i>1/m</i>.
|
| 649 |
|
|
</p>
|
| 650 |
|
|
|
| 651 |
|
|
<h6 align = "center">
|
| 652 |
|
|
<a name = "balls_and_bins">
|
| 653 |
|
|
<img src = "balls_and_bins.jpg" width = "70%" alt = "no image">
|
| 654 |
|
|
</a>
|
| 655 |
|
|
</h6>
|
| 656 |
|
|
<h6 align = "center">
|
| 657 |
|
|
Balls and bins.
|
| 658 |
|
|
</h6>
|
| 659 |
|
|
|
| 660 |
|
|
|
| 661 |
|
|
<p>
|
| 662 |
|
|
Denote the probability that a probe sequence of length <i>k</i>
|
| 663 |
|
|
appears in bin <i>i</i> by <i>p<sub>i</sub></i>, the length of the probe sequence
|
| 664 |
|
|
of bin <i>i</i> by <i>l<sub>i</sub></i>, and assume uniform distribution.
|
| 665 |
|
|
Then
|
| 666 |
|
|
</p>
|
| 667 |
|
|
<p>
|
| 668 |
|
|
<a name = "eqn:prob_of_p1">
|
| 669 |
|
|
<i>p<sub>1</sub>
|
| 670 |
|
|
= </i>(3)
|
| 671 |
|
|
</a>
|
| 672 |
|
|
</p>
|
| 673 |
|
|
<p>
|
| 674 |
|
|
<i>
|
| 675 |
|
|
<b>P</b>(l<sub>1</sub> ≥ k)
|
| 676 |
|
|
=
|
| 677 |
|
|
</i>
|
| 678 |
|
|
</p>
|
| 679 |
|
|
<p>
|
| 680 |
|
|
<i><b>P</b>(l<sub>1</sub> ≥ α ( 1 + k / α - 1 )
|
| 681 |
|
|
≤ </i>(a)
|
| 682 |
|
|
</p>
|
| 683 |
|
|
<p>
|
| 684 |
|
|
<i>
|
| 685 |
|
|
e
|
| 686 |
|
|
^
|
| 687 |
|
|
(
|
| 688 |
|
|
-
|
| 689 |
|
|
(
|
| 690 |
|
|
α ( k / α - 1 )<sup>2</sup>
|
| 691 |
|
|
)
|
| 692 |
|
|
/2
|
| 693 |
|
|
)
|
| 694 |
|
|
</i>
|
| 695 |
|
|
,
|
| 696 |
|
|
</p>
|
| 697 |
|
|
<p>
|
| 698 |
|
|
where (a) follows from the Chernoff bound
|
| 699 |
|
|
[<a href = "references.html#motwani95random">motwani95random</a>].
|
| 700 |
|
|
To
|
| 701 |
|
|
calculate the probability that <i>some</i> bin contains a probe
|
| 702 |
|
|
sequence greater than <i>k</i>, we note that the <i>l<sub>i</sub></i> are
|
| 703 |
|
|
negatively-dependent
|
| 704 |
|
|
[<a href = "references.html#dubhashi98neg">dubhashi98neg</a>].
|
| 705 |
|
|
Let <i><b>I</b>(.)</i>
|
| 706 |
|
|
denote the indicator function. Then
|
| 707 |
|
|
<p>
|
| 708 |
|
|
<a name = "eqn:at_least_k_i_n_some_bin">
|
| 709 |
|
|
<i><b>P</b>( exists<sub>i</sub> l<sub>i</sub> ≥ k )
|
| 710 |
|
|
= </i>(3)
|
| 711 |
|
|
</a>
|
| 712 |
|
|
</p>
|
| 713 |
|
|
<p>
|
| 714 |
|
|
<i>
|
| 715 |
|
|
<b>P</b>
|
| 716 |
|
|
(
|
| 717 |
|
|
∑ <sub>i = 1</sub><sup>m</sup>
|
| 718 |
|
|
<b>I</b>(l<sub>i</sub> ≥ k) ≥ 1
|
| 719 |
|
|
)
|
| 720 |
|
|
=
|
| 721 |
|
|
</i>
|
| 722 |
|
|
</p>
|
| 723 |
|
|
<p>
|
| 724 |
|
|
<i>
|
| 725 |
|
|
<b>P</b>
|
| 726 |
|
|
(
|
| 727 |
|
|
∑ <sub>i = 1</sub><sup>m</sup>
|
| 728 |
|
|
<b>I</b>
|
| 729 |
|
|
(
|
| 730 |
|
|
l<sub>i</sub> ≥ k
|
| 731 |
|
|
)
|
| 732 |
|
|
≥
|
| 733 |
|
|
m p<sub>1</sub> ( 1 + 1 / (m p<sub>1</sub>) - 1 )
|
| 734 |
|
|
)
|
| 735 |
|
|
≤ </i>(a)
|
| 736 |
|
|
</p>
|
| 737 |
|
|
<p>
|
| 738 |
|
|
<i>
|
| 739 |
|
|
e
|
| 740 |
|
|
^
|
| 741 |
|
|
(
|
| 742 |
|
|
(
|
| 743 |
|
|
-
|
| 744 |
|
|
m p<sub>1</sub>
|
| 745 |
|
|
(
|
| 746 |
|
|
1 / (m p<sub>1</sub>) - 1
|
| 747 |
|
|
)
|
| 748 |
|
|
<sup>2</sup>
|
| 749 |
|
|
)
|
| 750 |
|
|
/
|
| 751 |
|
|
2
|
| 752 |
|
|
)
|
| 753 |
|
|
,
|
| 754 |
|
|
</i>
|
| 755 |
|
|
</p>
|
| 756 |
|
|
<p>
|
| 757 |
|
|
where (a) follows from the fact that the Chernoff bound can be
|
| 758 |
|
|
applied to negatively-dependent variables
|
| 759 |
|
|
[<a href = "references.html#dubhashi98neg">dubhashi98neg</a>].
|
| 760 |
|
|
Inserting <a href = "#prob_of_p1">(2)</a> into
|
| 761 |
|
|
<a href = "#at_least_k_i_n_some_bin">(3)</a>, and equating with <i>1/m</i>,
|
| 762 |
|
|
we obtain
|
| 763 |
|
|
</p>
|
| 764 |
|
|
<p>
|
| 765 |
|
|
<i>
|
| 766 |
|
|
k
|
| 767 |
|
|
~
|
| 768 |
|
|
√
|
| 769 |
|
|
(
|
| 770 |
|
|
2 α </i>ln<i> 2 m </i>ln<i>(m) )
|
| 771 |
|
|
)
|
| 772 |
|
|
</i>
|
| 773 |
|
|
.
|
| 774 |
|
|
</p>
|
| 775 |
|
|
|
| 776 |
|
|
|
| 777 |
|
|
|
| 778 |
|
|
|
| 779 |
|
|
|
| 780 |
|
|
|
| 781 |
|
|
|
| 782 |
|
|
|
| 783 |
|
|
|
| 784 |
|
|
<h3><a name = "imp_pb_assoc">Implementation in <tt>pb_assoc</tt></a></h3>
|
| 785 |
|
|
|
| 786 |
|
|
<p>
|
| 787 |
|
|
The resize policies in the previous subsection are conceptually straightforward. The design
|
| 788 |
|
|
of hash-based containers' size-related interface is complicated by some factors.
|
| 789 |
|
|
</p>
|
| 790 |
|
|
<ol>
|
| 791 |
|
|
<li> Most containers, <i>i.e.</i> lists, trees, and vectors, have a single "size" concept. There is no
|
| 792 |
|
|
distinction between the number of entries the container holds and the number of entries it is using. This,
|
| 793 |
|
|
of course, is not the case for hash-based containers. Moreover, even describing the
|
| 794 |
|
|
"actual" size of a hash-based container (as opposed to its logical size) is difficult - a probing-based container
|
| 795 |
|
|
holds entries to elements, even those it does not use, while a chaining-based container holds pointers to entries.
|
| 796 |
|
|
</li>
|
| 797 |
|
|
<li>
|
| 798 |
|
|
The policies mentioned above operate in terms of invariants. <i>E.g.</i> a load-check trigger policy
|
| 799 |
|
|
maintains an invariant concerning the load factor of a container object. This is sometimes too rigid:
|
| 800 |
|
|
<ol>
|
| 801 |
|
|
<li>In some cases it is desirable to allow controlled override of an entire policy, <i>e.g.</i> by externally resizing a container object (or giving it an initial size, which is a special case of externally resizing the container).
|
| 802 |
|
|
</li>
|
| 803 |
|
|
<li>
|
| 804 |
|
|
In other cases it is desirable to allow changing the specifics of a policy in runtime, <i>e.g.</i>, changing the load factors of a load-check policy.
|
| 805 |
|
|
</li>
|
| 806 |
|
|
</ol>
|
| 807 |
|
|
</li>
|
| 808 |
|
|
<li>
|
| 809 |
|
|
Resize policies interact strongly with hash policies. Performance-wise, for example, it is undesirable to use an exponential size policy of powers of two with a modulo range-hashing function, and it is undesirable to use a prime size policy with a mask range-hashing function. In other cases, the effects are more dramatic. For example, using a quadratic probe function with an exponential size policy will probably cause cases where the container object has available entries which are never reached by the probe function. (<a href = "hash_policies.html">Hash Policies</a>
|
| 810 |
|
|
discusses the previous concepts.)
|
| 811 |
|
|
</li>
|
| 812 |
|
|
</ol>
|
| 813 |
|
|
|
| 814 |
|
|
<p>
|
| 815 |
|
|
Clearly, the more of these points an interface addresses, the greater its flexibility but the lower its encapsulation and uniformity between associative containers.
|
| 816 |
|
|
</p>
|
| 817 |
|
|
|
| 818 |
|
|
|
| 819 |
|
|
|
| 820 |
|
|
<p>
|
| 821 |
|
|
This library attempts to address these types of problems by delegating all size-related functionality to
|
| 822 |
|
|
policy classes. Hash-based containers
|
| 823 |
|
|
are parameterized by a resize-policy class (among others), and derive publicly from
|
| 824 |
|
|
the resize-policy class
|
| 825 |
|
|
[<a href = "references.html#alexandrescu01modern">alexandrescu01modern</a>]
|
| 826 |
|
|
<i>E.g.</i>, a collision-chaining
|
| 827 |
|
|
hash table is defined as follows:
|
| 828 |
|
|
</p>
|
| 829 |
|
|
<pre>
|
| 830 |
|
|
cc_ht_map<
|
| 831 |
|
|
<b>class</b> Key,
|
| 832 |
|
|
<b>class</b> Data,
|
| 833 |
|
|
...
|
| 834 |
|
|
<b>class</b> Resize_Policy
|
| 835 |
|
|
...> :
|
| 836 |
|
|
<b>public</b> Resize_Policy
|
| 837 |
|
|
</pre>
|
| 838 |
|
|
|
| 839 |
|
|
<p>
|
| 840 |
|
|
The containers themselves lack any functionality or public interface for manipulating sizes. A container
|
| 841 |
|
|
object merely forwards events to its resize policy object and queries it for needed actions.
|
| 842 |
|
|
</p>
|
| 843 |
|
|
|
| 844 |
|
|
<p>
|
| 845 |
|
|
Figure
|
| 846 |
|
|
<a href = "#insert_resize_sequence_diagram1">
|
| 847 |
|
|
Insert resize sequence diagram
|
| 848 |
|
|
</a>
|
| 849 |
|
|
shows a (possible) sequence diagram of an insert operation.
|
| 850 |
|
|
The user inserts an element; the hash table
|
| 851 |
|
|
notifies its resize policy that a search has started (point A);
|
| 852 |
|
|
in this case, a single collision is encountered - the table
|
| 853 |
|
|
notifies its resize policy of this (point B); the container
|
| 854 |
|
|
finally notifies its resize policy that the search has ended (point C);
|
| 855 |
|
|
it then queries its resize policy whether a resize is needed, and if so,
|
| 856 |
|
|
what is the new size (points D to G); following the resize, it notifies
|
| 857 |
|
|
the policy that a resize has completed (point H); finally, the element
|
| 858 |
|
|
is inserted, and the policy notified (point I).
|
| 859 |
|
|
</p>
|
| 860 |
|
|
|
| 861 |
|
|
<h6 align = "center">
|
| 862 |
|
|
<a name = "insert_resize_sequence_diagram1">
|
| 863 |
|
|
<img src = "insert_resize_sequence_diagram1.jpg" width = "70%" alt = "no image">
|
| 864 |
|
|
</a>
|
| 865 |
|
|
</h6>
|
| 866 |
|
|
<h6 align = "center">
|
| 867 |
|
|
Insert resize sequence diagram.
|
| 868 |
|
|
</h6>
|
| 869 |
|
|
|
| 870 |
|
|
<p>
|
| 871 |
|
|
This addresses, to some extent, the problems mentioned above:
|
| 872 |
|
|
</p>
|
| 873 |
|
|
<ol>
|
| 874 |
|
|
<li>
|
| 875 |
|
|
Different instantiations of range-hashing policies can be met with different instantiations of
|
| 876 |
|
|
resize policies.
|
| 877 |
|
|
</li>
|
| 878 |
|
|
<li>
|
| 879 |
|
|
Questions on size-related interface are avoided, since the containers have no size-related methods. Thus
|
| 880 |
|
|
a container has no method for querying its actual size. It merely continuously forwards enough information to
|
| 881 |
|
|
its resize policy to answer such queries; the designer of the resize policy can decide whether, or how, to design the appropriate method. Also, a container has no methods for setting its size. It merely queries its
|
| 882 |
|
|
resize policy for an initial size, queries it on a new size (if the resize policy indicates a resize is needed), and
|
| 883 |
|
|
supports a <tt><b>protected virtual</b></tt> function for external resize.
|
| 884 |
|
|
</li>
|
| 885 |
|
|
</ol>
|
| 886 |
|
|
|
| 887 |
|
|
<p>
|
| 888 |
|
|
The library contains a single class for instantiating a resize policy,
|
| 889 |
|
|
<tt>pb_assoc</tt> contains
|
| 890 |
|
|
a standard resize policy,
|
| 891 |
|
|
<a href = "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a> (the name is explained shortly).
|
| 892 |
|
|
In terms of interface, it is parameterized by a boolean constant indicating whether its public interface supports
|
| 893 |
|
|
queries of actual size and external resize operations (the inclusion and exclusion of these methods in the interface have obvious tradeoffs in terms of encapsulation and flexibility).
|
| 894 |
|
|
([<a href = "references.html#alexandrescu01modern">alexandrescu01modern</a>] shows many techniques for
|
| 895 |
|
|
changing between alternative interfaces at compile time.)
|
| 896 |
|
|
</p>
|
| 897 |
|
|
|
| 898 |
|
|
<p>
|
| 899 |
|
|
As noted before,
|
| 900 |
|
|
size and trigger policies are usually orthogonal.
|
| 901 |
|
|
<a href = "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a>
|
| 902 |
|
|
is parameterized by size and trigger policies. For example,
|
| 903 |
|
|
a collision-chaining hash table
|
| 904 |
|
|
is typically be defined as follows:
|
| 905 |
|
|
</p>
|
| 906 |
|
|
<pre>
|
| 907 |
|
|
cc_ht_map<
|
| 908 |
|
|
key,
|
| 909 |
|
|
data,
|
| 910 |
|
|
...
|
| 911 |
|
|
hash_standard_resize_policy<
|
| 912 |
|
|
some_trigger_policy,
|
| 913 |
|
|
some_size_policy,
|
| 914 |
|
|
...> >
|
| 915 |
|
|
</pre>
|
| 916 |
|
|
|
| 917 |
|
|
<p>
|
| 918 |
|
|
The sole function of
|
| 919 |
|
|
<a href = "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a>
|
| 920 |
|
|
is to
|
| 921 |
|
|
act as a standard delegator
|
| 922 |
|
|
[<a href = "references.html#gamma95designpatterns">gamma95designpatterns</a>] for these
|
| 923 |
|
|
policies.
|
| 924 |
|
|
|
| 925 |
|
|
<p>
|
| 926 |
|
|
Figures
|
| 927 |
|
|
<a href = "#insert_resize_sequence_diagram2">Standard resize policy trigger sequence diagram</a>
|
| 928 |
|
|
and
|
| 929 |
|
|
<a href = "#insert_resize_sequence_diagram3">Standard resize policy size sequence diagram</a>
|
| 930 |
|
|
show sequence diagrams illustrating the interaction between
|
| 931 |
|
|
the standard resize policy and its trigger and size policies, respectively.
|
| 932 |
|
|
</p>
|
| 933 |
|
|
|
| 934 |
|
|
<h6 align = "center">
|
| 935 |
|
|
<a name = "insert_resize_sequence_diagram2">
|
| 936 |
|
|
<img src = "insert_resize_sequence_diagram2.jpg" width = "70%" alt = "no image">
|
| 937 |
|
|
</a>
|
| 938 |
|
|
</h6>
|
| 939 |
|
|
<h6 align = "center">
|
| 940 |
|
|
Standard resize policy trigger sequence diagram.
|
| 941 |
|
|
</h6>
|
| 942 |
|
|
|
| 943 |
|
|
<h6 align = "center">
|
| 944 |
|
|
<a name = "insert_resize_sequence_diagram3">
|
| 945 |
|
|
<img src = "insert_resize_sequence_diagram3.jpg" width = "70%" alt = "no image">
|
| 946 |
|
|
</a>
|
| 947 |
|
|
</h6>
|
| 948 |
|
|
<h6 align = "center">
|
| 949 |
|
|
Standard resize policy size sequence diagram.
|
| 950 |
|
|
</h6>
|
| 951 |
|
|
|
| 952 |
|
|
<p>
|
| 953 |
|
|
The library (currently) supports the following instantiations of size
|
| 954 |
|
|
and trigger policies:
|
| 955 |
|
|
</p>
|
| 956 |
|
|
|
| 957 |
|
|
<ol>
|
| 958 |
|
|
<li>
|
| 959 |
|
|
<a href = "hash_load_check_resize_trigger.html"><tt>hash_load_check_resize_trigger</tt></a> implements
|
| 960 |
|
|
a load check trigger policy.
|
| 961 |
|
|
</li>
|
| 962 |
|
|
<li>
|
| 963 |
|
|
<a href = "cc_hash_max_collision_check_resize_trigger.html"><tt>cc_hash_max_collision_check_resize_trigger</tt></a>
|
| 964 |
|
|
implements a collision check trigger policy.
|
| 965 |
|
|
</li>
|
| 966 |
|
|
<li>
|
| 967 |
|
|
<a href = "hash_exponential_size_policy.html"><tt>hash_exponential_size_policy</tt></a> implemens
|
| 968 |
|
|
an exponential-size policy (which should be used with mask range hashing).
|
| 969 |
|
|
</li>
|
| 970 |
|
|
<li>
|
| 971 |
|
|
<a href = "hash_prime_size_policy.html"><tt>hash_prime_size_policy</tt></a> implementing
|
| 972 |
|
|
a size policy based on a sequence of primes
|
| 973 |
|
|
[<a href = "references.html#sgi_stl">sgi_stl</a>] (which should be used with mod range hashing
|
| 974 |
|
|
</li>
|
| 975 |
|
|
</ol>
|
| 976 |
|
|
|
| 977 |
|
|
<p>
|
| 978 |
|
|
The trigger policies also support interfaces for changing their specifics which depend on compile time constants.
|
| 979 |
|
|
</p>
|
| 980 |
|
|
|
| 981 |
|
|
|
| 982 |
|
|
<p>
|
| 983 |
|
|
Figure
|
| 984 |
|
|
<a href = "#resize_policy_cd">Resize policy class diagram</a> gives an overall picture
|
| 985 |
|
|
of the resize-related classes.
|
| 986 |
|
|
<tt>Container</tt> (which stands for any of the hash-based containers) is parameterized
|
| 987 |
|
|
by <tt>Resize_Policy</tt>, from which it subclasses publicly
|
| 988 |
|
|
[<a href = "references.html#alexandrescu01modern">alexandrescu01modern</a>].
|
| 989 |
|
|
This class is currently instantiated only by
|
| 990 |
|
|
<a href = "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a>.
|
| 991 |
|
|
<a href = "hash_standard_resize_policy.html"><tt>hash_standard_resize_policy</tt></a> itself
|
| 992 |
|
|
is parameterized by <tt>Trigger_Policy</tt> and <tt>Size_Policy</tt>.
|
| 993 |
|
|
Currently, <tt>Trigger_Policy</tt> is instantiated by
|
| 994 |
|
|
<a href = "hash_load_check_resize_trigger.html"><tt>hash_load_check_resize_trigger</tt></a>,
|
| 995 |
|
|
or
|
| 996 |
|
|
<a href = "cc_hash_max_collision_check_resize_trigger.html"><tt>cc_hash_max_collision_check_resize_trigger</tt></a>; <tt>Size_Policy</tt> is instantiated by
|
| 997 |
|
|
<a href = "hash_exponential_size_policy.html"><tt>hash_exponential_size_policy</tt></a>,
|
| 998 |
|
|
or
|
| 999 |
|
|
<a href = "hash_prime_size_policy.html"><tt>hash_prime_size_policy</tt></a>.
|
| 1000 |
|
|
</p>
|
| 1001 |
|
|
|
| 1002 |
|
|
|
| 1003 |
|
|
<h6 align = "center">
|
| 1004 |
|
|
<a name = "resize_policy_cd">
|
| 1005 |
|
|
<img src = "resize_policy_cd.jpg" width = "70%" alt = "no image">
|
| 1006 |
|
|
</a>
|
| 1007 |
|
|
</h6>
|
| 1008 |
|
|
<h6 align = "center">
|
| 1009 |
|
|
Resize policy class diagram.
|
| 1010 |
|
|
</h6>
|
| 1011 |
|
|
|
| 1012 |
|
|
|
| 1013 |
|
|
|
| 1014 |
|
|
|
| 1015 |
|
|
<h2><a name = "#policy_interaction">Policy Interaction</a></h2>
|
| 1016 |
|
|
|
| 1017 |
|
|
<p>
|
| 1018 |
|
|
Hash-tables are unfortunately susceptible to choice of policies. One
|
| 1019 |
|
|
of the more complicated aspects of this is that poor combinations of good policies
|
| 1020 |
|
|
can alter performance drastically. Following are some considerations.
|
| 1021 |
|
|
</p>
|
| 1022 |
|
|
|
| 1023 |
|
|
|
| 1024 |
|
|
|
| 1025 |
|
|
|
| 1026 |
|
|
|
| 1027 |
|
|
<h3>Range-Hashing Policies and Resize Policies</h3>
|
| 1028 |
|
|
|
| 1029 |
|
|
<p>
|
| 1030 |
|
|
</p>
|
| 1031 |
|
|
|
| 1032 |
|
|
|
| 1033 |
|
|
<h3>Equivalence Functors, Storing Hash Values, and Hash Functions</h3>
|
| 1034 |
|
|
|
| 1035 |
|
|
|
| 1036 |
|
|
<p>
|
| 1037 |
|
|
<a href = "cc_hash_assoc_cntnr.html"><tt>cc_hash_assoc_cntnr</tt></a>
|
| 1038 |
|
|
and
|
| 1039 |
|
|
<a href = "gp_hash_assoc_cntnr.html"><tt>gp_hash_assoc_cntnr</tt></a>
|
| 1040 |
|
|
are parameterized by an equivalenc functor and by a <tt>Store_Hash</tt>
|
| 1041 |
|
|
parameter. If the latter parameter is <tt><b>true</b></tt>, then
|
| 1042 |
|
|
the container stores with each entry a hash value, and uses
|
| 1043 |
|
|
this value in case of collisions to determine whether to apply a hash value.
|
| 1044 |
|
|
This can lower the cost of collision for some types, but increase the cost of collisions for other types.
|
| 1045 |
|
|
</p>
|
| 1046 |
|
|
|
| 1047 |
|
|
<p>
|
| 1048 |
|
|
If a ranged-hash function or ranged probe function is directly supplied, however,
|
| 1049 |
|
|
then it makes no sense to store the hash value with each entry. <tt>pb_assoc</tt>'s container will fail at compilation, by design, if this is attempted.
|
| 1050 |
|
|
</p>
|
| 1051 |
|
|
|
| 1052 |
|
|
|
| 1053 |
|
|
|
| 1054 |
|
|
</body>
|
| 1055 |
|
|
|
| 1056 |
|
|
</html>
|
